This handy Spectrum Math Grade 7 Answer Key Chapter 4 Lesson 4.5 Proportional Relationships on the Coordinate Plane provides detailed answers for the workbook questions.
Spectrum Math Grade 7 Chapter 4 Lesson 4.5 Proportional Relationships on the Coordinate Plane Answers Key
When proportional relationships are graphed, the points the line runs through can be used to find
the constant of proportionality.
This line runs through points (2, 2), (4, 4), (6, 6), and (8, 8).
First, find the proportion of this relationship by choosing one point and inserting its coordinates into the proportion equation.
k = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) k = \(\frac{4-2}{4-2}\) = \(\frac{2}{2}\) = 1
The constant of proportionality for this line is 1.
Find the constant of proportionality for each graph.
Question 1.
a.
k = _____
Answer: 0.667
k = 0.667
When proportional relationships are graphed, the points the line runs through can be used to find the constant of proportionality.
This line runs through points (3,2) and (6,4).
First, find the proportion of this relationship by choosing one point and inserting its coordinates into the proportion equation.
k = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) k = \(\frac{4-2}{6-3}\) = \(\frac{2}{3}\) = 0.667
The constant of proportionality for this line is 0.667
b.
k = _____
Answer: 0.334
k = 0.334
When proportional relationships are graphed, the points the line runs through can be used to find the constant of proportionality.
This line runs through points (3,1) and (9,3).
First, find the proportion of this relationship by choosing one point and inserting its coordinates into the proportion equation.
k = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) k = \(\frac{3-1}{9-3}\) = \(\frac{2}{6}\) = 0.334
The constant of proportionality for this line is 0.334
Question 2.
a.
k = _____
Answer: 3
k = 3
When proportional relationships are graphed, the points the line runs through can be used to find the constant of proportionality.
This line runs through points (1,3) and (2,6).
First, find the proportion of this relationship by choosing one point and inserting its coordinates into the proportion equation.
k = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) k = \(\frac{6-3}{2-1}\) = \(\frac{3}{1}\) = 3
The constant of proportionality for this line is 3.
b.
k = _____
Answer:
When proportional relationships are graphed, the points the line runs through can be used to find the constant of proportionality.
This line runs through points (4,3) and (8,6).
First, find the proportion of this relationship by choosing one point and inserting its coordinates into the proportion equation.
k = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) k = \(\frac{6-3}{8-4}\) = \(\frac{3}{4}\) = 0.
The constant of proportionality for this line is 3.
Find the constant of proportionality for each graph.
Question 1.
a.
k = _____
Answer: 5
k = 5
When proportional relationships are graphed, the points the line runs through can be used to find the constant of proportionality.
This line runs through points (1,5) and (2,10).
First, find the proportion of this relationship by choosing one point and inserting its coordinates into the proportion equation.
k = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) k = \(\frac{10-5}{2-1}\) = \(\frac{5}{1}\) = 5
The constant of proportionality for this line is 5.
b.
k = _____
Answer: 1
k = 1
When proportional relationships are graphed, the points the line runs through can be used to find the constant of proportionality.
This line runs through points (4,4) and (8,8).
First, find the proportion of this relationship by choosing one point and inserting its coordinates into the proportion equation.
k = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) k = \(\frac{8-4}{8-4}\) = \(\frac{4}{4}\) = 1
The constant of proportionality for this line is 1
Question 2.
a.
k = ____
Answer: 1.25
k = 1.25
When proportional relationships are graphed, the points the line runs through can be used to find the constant of proportionality.
This line runs through points (4,5) and (8,10).
First, find the proportion of this relationship by choosing one point and inserting its coordinates into the proportion equation.
k = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) k = \(\frac{10-5}{8-4}\) = \(\frac{5}{4}\) = 1.25
The constant of proportionality for this line is 1.25
b.
k = ____
Answer: 2
k = 2
When proportional relationships are graphed, the points the line runs through can be used to find the constant of proportionality.
This line runs through points (2,4) and (4,8).
First, find the proportion of this relationship by choosing one point and inserting its coordinates into the proportion equation.
k = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) k = \(\frac{8-4}{4-2}\) = \(\frac{4}{2}\) = 2
The constant of proportionality for this line is 2
Question 3.
a.
k = _____
Answer: 1.34
k = 1.34
When proportional relationships are graphed, the points the line runs through can be used to find the constant of proportionality.
This line runs through points (3,4) and (6,8).
First, find the proportion of this relationship by choosing one point and inserting its coordinates into the proportion equation.
k = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) k = \(\frac{8-4}{6-3}\) = \(\frac{4}{3}\) = 1.34
The constant of proportionality for this line is 1.34
b.
k = _____
Answer: 0.2
k = 0.2
When proportional relationships are graphed, the points the line runs through can be used to find the constant of proportionality.
This line runs through points (5,1) and (10,2).
First, find the proportion of this relationship by choosing one point and inserting its coordinates into the proportion equation.
k = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) k = \(\frac{2-1}{10-5}\) = \(\frac{1}{5}\) = 0.2
The constant of proportionality for this line is 0.2