Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations

It is essential for students to have the best material to study for the exams. Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations recommend to every student who wants to succeed in math. Fall in love with math by practicing the problems from Go Math 8th Grade Chapter 5 Writing Linear Equations Solution Key. We have provided the step by step explanations for each and every question in CCSS Math Answers. Quick & smart learning is possible with the Go Math Grade 8 Answer Key Chapter 5 Writing Linear EquationsPDF.

Go Math Grade 8 Chapter 5 Writing Linear Equations Answer Key

The students who are willing to become masters in maths are suggested to follow our Go Math 8th Grade Chapter 5 Writing Linear Equations Solution Key. You can get free access to Go Math Grade 8 Answer Key Chapter 5 Writing Linear equations topic-wise here. Check out the topics of Writing Linear equations from the below section.

Lesson 1: Writing Linear Equations from Situations and Graphs 

Lesson 2: Writing Linear Equations from a Table

Lesson 3: Linear Relationships and Bivariate Data

Model Quiz

Mixed Review

Guided Practice – Writing Linear Equations from Situations and Graphs – Page No. 130

Question 1.
Li is making beaded necklaces. For each necklace, she uses 27 spacers, plus 5 beads per inch of necklace length. Write an equation to find how many beads Li needs for each necklace.
a. input variable:
____________

Answer:
The length of the necklace in inches

Question 1.
b. output variable:
____________

Answer:
The total number of beads in the necklace

Question 1.
c. equation:
Type below:
____________

Answer:
y = 5x

Question 2.
Kate is planning a trip to the beach. She estimates her average speed to graph her expected progress on the trip. Write an equation in slope-intercept form that represents the situation.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 1: Writing Linear Equations from Situations and Graphs img 1
Type below:
____________

Answer:
y = -60x + 300

Explanation:
Choose two points on the graph to find the slope.
Find the slope
m = (y2 -y1)/(x2 – x1)
m = -300/5 = -60
Read the y-intercept from the graph: b = 300
Use your slope and y-intercept values to write an equation in slope-intercept
form.
y = -60x + 300

Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Page 130 Q3

Essential Question Check-In

Question 4.
Explain what m and b in the equation y = mx + b tell you about the graph of the line with that equation.
Type below:
____________

Answer:
The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept.
m = change in y-value/change in x-value
The y-intercept of this line is the value of y at the point where the line crosses the y-axis.

Independent Practice – Writing Linear Equations from Situations and Graphs – Page No. 131

Question 5.
A dragonfly can beat its wings 30 times per second. Write an equation in slope-intercept form that shows the relationship between flying time in seconds and the number of times the dragonfly beats its wings
Type below:
____________

Answer:
y = 30x

Explanation:
The linear equation is y = mx + b where m is the slope and b is the y-intercept.
y variable will be the number of times the dragonfly has beat its wings and the x variable will be the time.
A dragonfly can beat its wings 30 times per second.
To find b, let’s consider how many times the dragonfly has beat its wings at time 0s.
So, the equation of the line is y = 30x

Question 6.
A balloon is released from the top of a platform that is 50 meters tall. The balloon rises at the rate of 4 meters per second. Write an equation in slope-intercept form that tells the height of the balloon above the ground after a given number of seconds.
Type below:
____________

Answer:
y = 4x + 50

Explanation:
Input variable: Number of seconds
Output variable: Height of the balloon
The balloon rises at a rate of 4 meters per second. m = 4;
A balloon is released from the top of a platform that is 50 meters tall. b = 50.
y = 4x + 50

The graph shows a scuba diver’s ascent over time.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 1: Writing Linear Equations from Situations and Graphs img 2

Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Page 131 Q7

Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Page 131 Q8

Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Page 131 Q9

Question 10.
The formula for converting Celsius temperatures to Fahrenheit temperatures is a linear equation. Water freezes at 0°C, or 32°F, and it boils at 100°C, or 212°F. Find the slope and y-intercept for a graph that gives degrees Celsius on the horizontal axis and degrees Fahrenheit on the vertical axis. Then write an equation in slope-intercept form that converts degrees Celsius into degrees Fahrenheit.
Type below:
____________

Answer:
Input variable: Celsius
Output variable: Fahrenheit
(0, 32) (100, 212)
m = (y2 -y1)/(x2 – x1) = (212 – 32)/(100 – 0) = 180/100 = 1.8
y-intercepts = 32 when x = 0
F = 1.8C + 32

Question 11.
The cost of renting a sailboat at a lake is $20 per hour plus $12 for lifejackets. Write an equation in slope-intercept form that can be used to calculate the total amount you would pay for using this sailboat.
Type below:
____________

Answer:
y = 20x + 12

Explanation:
Input variable: Number of hours the sailboat is rented
Output variable: Total cost
The cost of renting a sailboat at a lake is $20 per hour plus $12 for lifejackets.
Slope m = 20; y-intercept b = 12
Substituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 20 and b = 12.
y = 20x + 12

Writing Linear Equations from Situations and Graphs – Page No. 132

The graph shows the activity in a savings account.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 1: Writing Linear Equations from Situations and Graphs img 3

Question 12.
What was the amount of the initial deposit that started this savings account?
$ _______

Answer:
$1000

Explanation:
The amount of the initial deposit that started this savings account is $1000

Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Page 132 Q13

Question 14.
Write an equation in slope-intercept form for the activity in this savings account.
Type below:
____________

Answer:
y = 500x + 1000

Explanation:
Substituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 500 and b = 1000.
y = 500x + 1000

Question 15.
Explain the meaning of the slope in this graph.
Type below:
____________

Answer:
The slope represents the money saved in dollars per month in the plan.

H.O.T.

Focus on Higher Order Thinking

Question 16.
Communicate Mathematical Ideas
Explain how you decide which part of a problem will be represented by the variable x, and which part will be represented by the variable y in a graph of the situation.
Type below:
____________

Answer:
y=mx+b
M-slope
B-Y intercept
and
(x,y)- would be any point on the graph and if you were to plug those points in for x and y the equation would solve if done properly

Question 17.
Represent Real-World Problems
Describe what would be true about the rate of change in a situation that could not be represented by a graphed line and an equation in the form y = mx + b.
Type below:
____________

Answer:
The rate of change would not be constant. Using different pairs of points in the slope formula would give different results.

Question 18.
Draw Conclusions
Must m, in the equation y = mx + b, always be a positive number? Explain.
Type below:
____________

Answer:
No; The slope m can be negative or positive. If the slope of the number is positive (the graph goes upward from left to right), then m will be positive, but if the slope is negative (the graph goes down from left to right), then m is negative.

Guided Practice – Writing Linear Equations from a Table – Page No. 136

Question 1.
Jaime purchased a $20 bus pass. A certain amount is deducted from the pass each time he rides the bus. The table shows the amount, y, left on his pass after x rides. Graph the data, and find the slope and y-intercept from the graph or from the table. Then write the equation for the graph in slope-intercept form.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 2: Writing Linear Equations from a Table img 4
Type below:
____________

Answer:
Grade 8 Chapter 5 image 1
y = -5/4 x + 20

Explanation:
Slope = -20/16 = -5/4 = -1.25
y-intercepts = 20
Substituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = -1.25 and b = 20.
y = -5/4 x + 20

The table shows the temperature (y) at different altitudes (x). This is a linear relationship.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 2: Writing Linear Equations from a Table img 5

Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Page 136 Q2

Question 3.
Find the y-intercept for this relationship.
y-intercept = _______

Answer:
b = 50

Explanation:
y-intercept = 59 when x = 0

Question 4.
Write an equation in slope-intercept form that represents this relationship.
Type below:
____________

Answer:
y = -0.004x + 59

Explanation:
Substituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = -0.004 and b = 59.

Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Page 136 Q5

Essential Question Check-In

Question 6.
Describe how you can use the information in a table showing a linear relationship to find the slope and y-intercept for the equation.
Type below:
____________

Answer:
Use any two points from the table to find the slope.
Slope m = (y2 -y1)/(x2 – x1)
If the value of y-intercept, when x=0 is not given in the table, use the slope and any ordered pair from the table and substitute in slope-intercept form y=mx + b to find b.

Independent Practice – Writing Linear Equations from a Table – Page No. 137

Question 7.
The table shows the costs of a large cheese pizza with toppings at a local pizzeria. Graph the data, and find the slope and y-intercept from the graph. Then write the equation for the graph in slope-intercept form.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 2: Writing Linear Equations from a Table img 6
Type below:
____________

Answer:
Grade 8 Chapter 5 image 2

Slope m = (y2 -y1)/(x2 – x1) = (10 – 8)/(1 – 0) = 2/1 = 2
y-intercept b = 8
Substituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 2 and b = 8.
y = 2x + 8

Question 8.
The table shows how much an air-conditioning repair company charges for different numbers of hours of work. Graph the data, and find the slope and y-intercept from the graph. Then write the equation for the graph in slope-intercept form.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 2: Writing Linear Equations from a Table img 7
Type below:
____________

Answer:
Grade 8 Chapter 5 image 3

Slope m = (y2 -y1)/(x2 – x1) = (100 – 50)/(1 – 0) = 50/1 = 50
y-intercept b = 50
Substituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 50 and b = 50.
y = 50x + 50

Question 9.
A friend gave Ms. Morris a gift card for a local car wash. The table shows the linear relationship of how the value left on the card relates to the number of car washes.
a. Write an equation that shows the number of dollars left on the card.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 2: Writing Linear Equations from a Table img 8
Type below:
____________

Answer:
y = -1.50x + 30

Explanation:
Slope m = (y2 -y1)/(x2 – x1) = (18 – 30)/(8 – 0) = -12/8 = -1.5
y-intercept b = 30
Substituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = -1.50 and b = 30.
y = -1.50x + 30

Question 9.
b. Explain the meaning of the negative slope in this situation.
Type below:
____________

Answer:
The negative slope means that the amount on the card decreased by $1.5 per car wash

Question 9.
c. What is the maximum value of x that makes sense in this context? Explain.
x = _______

Answer:
x = 20

Explanation:
0 = -1.50x + 30
1.5x = 30
x = 30/1.5 = 20
the maximum value of x = 20

The tables show linear relationships between x and y. Write an equation in slope-intercept form for each relationship.

Question 10.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 2: Writing Linear Equations from a Table img 9
Type below:
____________

Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Page 137 Q10

Question 11.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 2: Writing Linear Equations from a Table img 10
Type below:
____________

Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Page 137 Q11

Writing Linear Equations from a Table – Page No. 138

Question 12.
Finance
Desiree starts a savings account with $125.00. Every month, she deposits $53.50.
a. Complete the table to model the situation.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 2: Writing Linear Equations from a Table img 11
Type below:
____________

Answer:
Grade 8 Chapter 5 image 4

Question 12.
b. Write an equation in slope-intercept form that shows how much money Desiree has in her savings account after x months.
Type below:
____________

Answer:
y = 53.5x + 125

Explanation:
Desiree starts a savings account with $125.00. Every month, she deposits $53.50.
Substituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 53.5 and b = 125.
y = 53.5x + 125

Question 12.
c. Use the equation to find how much money Desiree will have in savings after 11 months.
$ ________

Answer:
$713.5

Explanation:
y = 53.5x + 125
The value of x is 11
y = 53.5 (11) + 125 = 588.5 + 125 = 713.5
Desiree will have $713.5 in savings after 11 months.

Question 13.
Monty documented the amount of rain his farm received on a monthly basis, as shown in the table.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 2: Writing Linear Equations from a Table img 12
a. Is the relationship linear? Why or why not?
Type below:
____________

Answer:
No

Explanation:
The change in the months is constant but the change in rainfall is not constant.

Question 13.
b. Can an equation be written to describe the amount of rain? Explain.
Type below:
____________

Answer:
No

Explanation:
There is no apparent pattern in the given data.

H.O.T.

Focus on Higher Order Thinking

Question 14.
Analyze Relationships
If you have a table that shows a linear relationship, when can you read the value for b, in y = mx + b, directly from the table without drawing a graph or doing any calculations? Explain.
Type below:
____________

Answer:
You can read the value of b directly from the table when the table contains the input value of 0 and its corresponding output values (value of y when x = 0)

Question 15.
What If?
Jaíme graphed linear data given in the form (cost, number). The y-intercept was 0. Jayla graphed the same data given in the form (number, cost). What was the y-intercept of her graph? Explain.
Type below:
____________

Answer:
Jaíme graphed linear data given in the form (cost, number). The y-intercept was 0. Jayla graphed the same data given in the form (number, cost).
Jaíme’s graph contained (0, 0). Since Jayal’s data were the same y-intercept is 0 but x and y are switched.

Guided Practice – Linear Relationships and Bivariate Data – Page No. 144

Use the following graphs to find the equation of the linear relationship.

Question 1.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 3: Linear Relationships and Bivariate Data img 13
Type below:
____________

Answer:
y = 30x

Explanation:
Grade 8 Chapter 5 image 5
Find the slope using two points from the grapgh by
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (1, 30) and (x2, y2) = (2, 60)
Slope m = (y2 -y1)/(x2 – x1) = (60 – 30)/(2 – 1) = 30/1 = 30
y-intercept b = 0
Substituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 30 and b = 0.
y = 30x

Question 2.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 3: Linear Relationships and Bivariate Data img 14
Type below:
____________

Answer:
y = 2.5x + 2

Explanation:
Grade 8 Chapter 5 image 6
Find the slope using two points from the grapgh by
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (2, 7) and (x2, y2) = (4, 12)
Slope m = (y2 -y1)/(x2 – x1) = (12 – 7)/(4 – 2) = 5/2 = 2.5
y-intercept b = 2
Substituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 2.5 and b = 2.
y = 2.5x + 2

Question 3.
The graph shows the relationship between the number of hours a kayak is rented and the total cost of the rental. Write an equation of the relationship. Then use the equation to predict the cost of a rental that lasts 5.5 hours.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 3: Linear Relationships and Bivariate Data img 15
Type below:
____________

Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Page 144 Q3

Does each of the following graphs represent a linear relationship? Why or why not?

Question 4.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 3: Linear Relationships and Bivariate Data img 16
____________

Answer:
Yes; The graph has a constant rate of change

Explanation:
Find the slope using two points from the graph by
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (2, 6) and (x2, y2) = (5, 15)
Slope m = (y2 -y1)/(x2 – x1) = (15 – 6)/(5 – 2) = 9/3 = 3
y-intercept b = 6
Substituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 3 and b = 6.
y = 3x + 6
The values changing according to the constant change in the x values.

Question 5.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 3: Linear Relationships and Bivariate Data img 17
____________

Answer:
No; The graph does not have a constant rate of change

Essential Question Check-In

Question 6.
How can you tell if a set of bivariate data shows a linear relationship?
Type below:
____________

Answer:
It is a linear relationship if the rate of change is constant or the graph is straight.

Independent Practice – Linear Relationships and Bivariate Data – Page No. 145

Does each of the following tables represent a linear relationship? Why or why not?

Question 7.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 3: Linear Relationships and Bivariate Data img 18
____________

Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Page 145 Q7

Question 8.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 3: Linear Relationships and Bivariate Data img 19
____________

Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Page 145 Q8

Explain whether or not you think each relationship is linear.

Question 9.
the cost of equal-priced DVDs and the number purchased
____________

Answer:
y = cx

Explanation:
The relation between the cost of equal-priced DVDs and the number purchased is linear because the change rate is constant. If we denote with c the cost of a DVD, with x the number of purchased DVDs and with y the total cost of the purchased DVDs, we get an equation of the form:
y = cx

Question 10.
the height of a person and the person’s age
____________

Answer:
Non-Linear relationship

Explanation:
The height of a person does not increase at a constant rate with a person’s age

Question 11.
the area of a square quilt and its side length
____________

Answer:
Non-Linear relationship

Explanation:
The rate of change in the area of a square quilt increases as the side length increases.

Question 12.
the number of miles to the next service station and the number of kilometers
____________

Answer:
Linear relationship

Explanation:
The number of miles increases at a constant rate with the number of kilometers.

Question 13.
Multistep
The Mars Rover travels 0.75 feet in 6 seconds. Add the point to the graph. Then determine whether the relationship between distance and time is linear, and if so, predict the distance that the Mars Rover would travel in 1 minute.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 3: Linear Relationships and Bivariate Data img 20
Distance traveled in 1 min.: _______ ft.

Answer:
Relationship is linear
Distance traveled in 1 min.: 7.5 ft.

Explanation:
Grade 8 Chapter 5 image 7
The graph is a straight line. So, the Relationship is linear
The equation representing the relationship between distance and time.
y = 0.125x
The value of x is 1 min = 60 sec
y = 0.125 (60) = 7.5 ft
Distance traveled in 1 min.: 7.5 ft.

Linear Relationships and Bivariate Data – Page No. 146

Question 14.
Make a Conjecture
Zefram analyzed a linear relationship, found that the slope-intercept equation was y=3.5x+16, and made a prediction for the value of y for a given value of x. He realized that he made an error calculating the y-intercept and that it was actually 12. Can he just subtract 4 from his prediction if he knows that the slope is correct? Explain.
____________

Answer:
Yes

Explanation:
The value of y is calculated using y = 3.5x+ 16. Since the slope of the point remains the same, 4 can be subtracted from the predicted answer as the value of y would be: y = 3.5x+ 16 – 4

H.O.T.

Focus on Higher Order Thinking

Question 15.
Communicate Mathematical Ideas
The table shows a linear relationship. How can you predict the value of y when x = 6 without finding the equation of the relationship?
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 3: Linear Relationships and Bivariate Data img 21
Type below:
____________

Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Page 146 Q15

Question 16.
Critique Reasoning
Louis says that if the differences between the values of x are constant between all the points on a graph, then the relationship is linear. Do you agree? Explain.
____________

Answer:
No

Explanation:
The difference between y should be constant for a constant interval of x.

Question 17.
Make a Conjecture
Suppose you know the slope of a linear relationship and one of the points that its graph passes through. How could you predict another point that falls on the graph of the line?
Type below:
____________

Answer:
Find the equation of the linear relationship using the slope and given point. Insert any x-value to find a y-value on the graph of the line.

Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Page 146 Q18

5.1 Writing Linear Equations from Situations and Graphs – Model Quiz – Page No. 147

Write the equation of each line in slope-intercept form.

Question 1.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Model Quiz img 22
Type below:
____________

Answer:
y = 30x + 20

Explanation:
Find the slope using two points from the graph by m = (y2 -y1)/(x2 – x1) where (x1, y1) = (0, 20), (x2, y2) = (2, 80)
Substitute the value of m and (x1, y1) = (0, 20), (x2, y2) = (2, 80)
Slope m = (y2 -y1)/(x2 – x1) = (80 – 20)/(2 – 0) = 60/2 = 30
Substituting the value of slope (m) and (x, y) in the slope-intercept form to find y-intercept (b):
80 = 30(2) + b
y-intercept b = 20
Substituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 30 and b = 20.
y = 30x + 20

Question 2.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Model Quiz img 23
Type below:
____________

Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Page 147 Q2

5.2 Writing Linear Equations from a Table

Write the equation of each linear relationship in slope-intercept form.

Question 3.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Model Quiz img 24
Type below:
____________

Answer:
y = 0.35x + 1.5

Explanation:
Find the slope using two points from the graph by m = (y2 -y1)/(x2 – x1) where (x1, y1) = (0, 1.5), (x2, y2) = (100, 36.5)
Substitute the value of m and (x1, y1) = (0, 1.5), (x2, y2) = (100, 36.5)
Slope m = (y2 -y1)/(x2 – x1) = (36.5 – 1.5)/(100 – 0) = 35/100 = 0.35
Substituting the value of slope (m) and (x, y) in the slope-intercept form to find y-intercept (b):
1.5 =0.35(0) + b
y-intercept b = 1.5
Substituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 0.35 and b = 1.5.
y = 0.35x + 1.5

Question 4.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Model Quiz img 25
Type below:
____________

Answer:
y = -0.6x + 109

Explanation:
Find the slope using two points from the graph by m = (y2 -y1)/(x2 – x1) where (x1, y1) = (25, 94), (x2, y2) = (35, 88)
Substitute the value of m and (x1, y1) = (25, 94), (x2, y2) = (35, 88)
Slope m = (y2 -y1)/(x2 – x1) = (88 – 94)/(35 – 25) = -6/10 = -0.6
Substituting the value of slope (m) and (x, y) in the slope-intercept form to find y-intercept (b):
88 = -0.6(35) + b
y-intercept b = 109
Substituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = -0.6 and b = 109.
y = -0.6x + 109

5.3 Linear Relationships and Bivariate Data

Write the equation of the line that connects each set of data points.

Question 5.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Model Quiz img 26
Type below:
____________

Answer:
y = 2/3x + 26 2/3

Explanation:
Grade 8 Chapter 5 image 8
Find the slope using two points from the graph by m = (y2 -y1)/(x2 – x1) where (x1, y1) = (20, 40), (x2, y2) = (50, 60)
Substitute the value of m and (x1, y1) = (20, 40), (x2, y2) = (50, 60)
Slope m = (y2 -y1)/(x2 – x1) = (60 – 40)/(50 – 20) = 20/30 = 2/3
Substituting the value of slope (m) and (x, y) in the slope-intercept form to find y-intercept (b):
40 = 2/3(20) + b
y-intercept b = 26 2/3
Substituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 2/3 and b = 26 2/3.
y = 2/3x + 26 2/3

Question 6.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Model Quiz img 27
Type below:
____________

Answer:
y = -3x + 140

Explanation:
Grade 8 Chapter 5 image 9
Find the slope using two points from the graph by m = (y2 -y1)/(x2 – x1) where (x1, y1) = (25, 65), (x2, y2) = (30, 50)
Substitute the value of m and (x1, y1) = (25, 65), (x2, y2) = (30, 50)
Slope m = (y2 -y1)/(x2 – x1) = (50 – 65)/(30 – 25) = -15/5 = -3
Substituting the value of slope (m) and (x, y) in the slope-intercept form to find y-intercept (b):
50 = -3(30) + b
y-intercept b = 140
Substituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = -3 and b = 140.
y = -3x + 140

Essential Question

Question 7.
Write a real-world situation that can be represented by a linear relationship.
Type below:
____________

Answer:
There is an hourly fee of $15 for renting the ski gear per hour and an entry fee of $10 for the ski lodge.

Selected Response – Mixed Review – Page No. 148

Question 1.
An hourglass is turned over with the top part filled with sand. After 3 minutes, there is 855 mL of sand in the top half. After 10 minutes, there is 750 mL of sand in the top half. Which equation represents this situation?
Options:
a. y = 285x
b. y = −10.5x + 900
c. y = −15x + 900
d. y = 75x

Answer:
c. y = −15x + 900

Explanation:
Identify the input and output variable
Input: Number of minutes
Output: Quantity of sand in the hourglass
Write the given information as ordered pair (3, 855), (10, 750)
Find the slope using two points from the graph by m = (y2 -y1)/(x2 – x1) where (x1, y1) = (10, 750), (x2, y2) =(3, 855)
Substitute the value of m and (x1, y1) = (10, 750), (x2, y2) =(3, 855)
Slope m = (y2 -y1)/(x2 – x1) = (855 – 750)/(3 – 10) = -105/7 = -15
Substituting the value of slope (m) and (x, y) in the slope-intercept form to find y-intercept (b):
750 = -15(10) + b
y-intercept b = 900
Substituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = -15 and b = 900.
y = -15x + 900

Question 2.
Which graph shows a linear relationship?
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Mixed Review img 28
Options:
a. A
b. B
c. C
d. D

Answer:
b. B

Explanation:
Graph B represents the linear relationship
The data appears to lie in a straight line

Question 3.
What are the slope and y-intercept of the relationship shown in the table?
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Mixed Review img 29
Options:
a. slope = 0.05, y-intercept = 1,500
b. slope = 0.5, y-intercept = 1,500
c. slope = 0.05, y-intercept = 2,000
d. slope = 0.5, y-intercept = 2,000

Answer:
c. slope = 0.05, y-intercept = 2,000

Explanation:
Find the slope using two points from the graph by m = (y2 -y1)/(x2 – x1) where (x1, y1) = (10,000, 2,500), (x2, y2) =(20,000, 3,000)
Substitute the value of m and (x1, y1) = (10,000, 2,500), (x2, y2) =(20,000, 3,000)
Slope m = (y2 -y1)/(x2 – x1) = (3,000 – 2,500)/(20,000 – 10,000) = 500/10,000 = 0.05
Substituting the value of slope (m) and (x, y) in the slope-intercept form to find y-intercept (b):
3,000 = 0.05(20,000) + b
y-intercept b = 2,000

Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Page 148 Q4

Mini-Task

Question 5.
Franklin’s faucet was leaking, so he put a bucket underneath to catch the water. After a while, Franklin started keeping track of how much water was in the bucket. His data is in the table below.
Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Mixed Review img 30
a. Is the relationship linear or nonlinear?
_____________

Answer:
The relationship linear

Explanation:
Find the rate of change by Difference in Quarts/Hours
(6.5 – 5)/(3 – 2) = 1.5
(8 – 6.5)/(4 – 3) = 1.5
(9.5 – 8)/(5 – 4) = 1.5
Since the rate of change is constant, the relationship is linear.

Question 5.
b. Write the equation for the relationship.
Type below:
_____________

Answer:
Rate of change is the slope of the linear equation
m = 1.5

Question 5.
c. Predict how much water will be in the bucket after 14 hours if Franklin doesn’t stop the leak.
_______ quarts

Answer:
23 quarts

Explanation:
Substituting the value of slope (m) and (x, y) in the slope-intercept form to find y-intercept (b)
y = mx + b
5 = 1.5(2) + b
y-intercept b = 2
Substituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 1.5 and b = 2.
y = 1.5x + 2
The x value is 2
y = 1.5(2) + 2 = 23
There will be 23 quarts after 14 hrs.

Conclusion:

Every expert’s choice is utilizing Go Math Grade 8 Chapter 5 Writing Linear Equations Answer Key PDF. Practice the question from our Go Math 8th Grade Chapter 5 Writing Linear Equations Answers to score the highest marks in the exams. Compare the questions with the real-time problems and solve the problems with the help of Go Math Grade 8 Chapter 5 Answer Key Chapter 5 Writing Linear Equations. Stay tuned to our ccssanswers.com to get the all Go Math Grade 8 Answer Key Chapterwise pdf.

Leave a Comment