Worksheet on Slope and Y-intercept with stepwise solutions are available here. So, the students who are all in search of the concept of slope and Y-intercept in coordinate geometry can make use of this slope and y intercept worksheets with answer key pdf and practice the problems. You can find different types of problems related to the slope (m) and y-intercept. Look into the problems given below in the slope and y intercept worksheet with answers and enhance your math skills.
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Identifying Slope and Y Intercept Worksheet PDF
Example 1.
Find the slope of the line joining the points (4,−6) and (5,−2).
Solution:
Let A(4,−8) and B(5,−2) be two points.
Slope of the line = y2 – y1/x2 – x1
= -2-(-6)/5 – 4
= -2+6/1
= 4/1
= 4
Therefore the slope of the given points are 4.
Example 2.
If the slope of the line joining the points A(x,3) and B(6,−8) is -6/4, find the value of x.
Solution:
Given that the two points are
A(x,3) and B(6,-8)
x1 = x, y1 = 3, x2 = 6, y2 = -8
Given slope = -6/4
We know that
x2 – x1/y2 – y1
6 – x/-8 – 3 = -6/4
6 – x/-11 = -6/4
24 – 4x = -66
24 + 66 = 4x
90 = 4x
x = 90/4
Hence the value of x = 90/4
Example 3.
The following points are plotted in the x-y plane. Find the slope and y-intercept of the line joining each pair of (1,4) & (-2,3).
Solution:
Given that the points are (1,4) and (-2,3)
x1 = 1, y1 = 4, x2 = -2 and y2 = 3
slope is (y2-y1)/(x2-x1)
(3 – 4)/(-2-1)
= -1/-3
Slope = 1/3
then y=mx+c
you get x-3y+4=0
at y axis x=0
y = 4/3
Therefore y-intercept = 4/3
Example 4.
Find the slope of the line, which makes an angle of 40° with the positive direction of the y-axis measured anticlockwise.
Solution:
If a line makes an angle of 40° with the positive direction of the y-axis measured anticlockwise, then the angle made by the line with the positive direction of the x-axis measured anticlockwise is 90° +40° = 130°
Thus, the slope of the given line is
tan 130°
= tan(180° – 50°)
= −tan50°
= − 1.19175
Example 5.
Determine the slope and y-intercept of the line 4x + 16y + 10 = 0
Solution:
Given that the equation is 4x + 16y + 10 = 0
16y = – 4x – 10
y = -4/16x – 10/16
y = -1/4x – 5/8.
Comparing this with y = mx + c,
Then we get m = – 1/4 and c = – 5/8
Therefore, slope = -1/4 and y-intercept = -5/8
Example 6.
The points (-3, 3) and (1, -4) are plotted in the x-y plane. Find the slope and y-intercept of the line joining the points.
Solution:
Let the line graph obtained by joining the points are (-3, 3) and (1, -4) be the graph of y = mx + c.
So, the given pairs of values of (x, y) obey the relation y = mx + c.
Therefore, 3 = -3m + c …….(i)
-4 = m + c …… (ii)
Subtracting (ii) from (i),
then we get
3 + 3 = -2m – m
9 = -3m
-3m = 9
m = 9/-3
m = -3
Putting m = -3 in (ii),
Then
-4 = -3 + c
c = -1.
Now, m = -3
The slope of the line graph = -3,
c = -1
The y-intercept of the line graph = -1
Example 7.
Find the slope and y-intercept of 3x – √4y = 2√4
Solution:
Given that the equation is 3x – √3y = 2√4
– √4y = -3x + 2√4
√4y = 3x – 2√4
y = 3/√4x – 2√4/√4
y = 3/√4x – 2
Comparing the above equation with y = mx + c,
Then the slope m = 3/√4 and y-intercept = -2.
Example 8.
Find the equation of a line in the form of y = mx + c, having a slope of 10 units and an intercept of -12 units.
Solution:
Given that
The slope of the line, m = 10, and The y-intercept of the line, c = -12.
We know that
The slope-intercept form of the equation of a line is y = mx + c.
From the equation
y = 10x – 12
Therefore the required equation of the line is y = 10x – 12.
Example 9.
Determine the slope and y-intercept of the line 4y + 12 = 0
Solution:
Given that the equation is
4y + 12 = 0
4y = -12
y = -12/4
y = 0 and x = -3
Comparing with y = mx + c,
Then we get m = 0 and c = -3
Therefore, slope = 0 and y-intercept = -3
Example 10.
What is the y-intercept of the graph of 2x + 7y = 6?
Solution:
Given that the equation is 2x + 7y = 6
7y = -2x + 6
y = – 2/7x + 6/7
We know that
y = mx + c,
Comparing the equation with y = mx + c
we get c = 13/4. So, the y-intercept = 13/4
and m = -2/7 therefore slope = -2/7