Problems on Slope and Y-intercept with step-by-step explanations are available here. The equation of the slope-intercept form is y = mx + c. An intercept is a point on the y-axis by which the slope of the line passes. The point where the line crosses the x-axis is known as the x-intercept and the point where the line crosses the y-axis is known as the y-intercept. The Problems on Slope and Y-intercept in coordinate geometry is a combination of different types of questions. Start practicing the problems on slope-intercept from this page and score good marks in the exams.
Also Read:
- Worksheet on Slope and Y-intercept
Slope and Y-Intercept Form Problems with Solutions
Example 1.
Determine the slope and y-intercept of the line 6x – 5y + 7 = 0
Solution:
Given that the equation is 6x – 5y – 7 = 0
-5y = -6x + 7
y = −6/−5x + 7/−5.
y = 6/5x – 7/5.
Comparing this with y = mx + c, we have: m = 6/5 and c = -7/5
Therefore, slope = 6/5 and y-intercept = -7/5
Example 2.
What is the slope and y-intercept of the equation 2x – 3y + 4 = 0?
Solution:
Given that the equation is
2x – 3y + 4 = 0
3y = 2x + 4
y = 2/3x + 4/3.
y = 2/3x + 4/3
Comparing the equation with y = mx + c,
we have m = 2/3.
Therefore, the slope of the line is 4/3.
Example 3.
Find the slope and y-intercept of the equation √3x – 3y + 8 = 0
Solution:
Given that the equation is √3x – 3y + 8 = 0
3y = √3x + 8
y = √3/3x + 8/3
Comparing with the equation y = mx + c
Then we have m = √3/3 and c = 8/3
Therefore the slope = √3/3 and y-intercept = 8/3.
Example 4.
What is the slope and y-intercept of the equation 6x – 7y + 8 = 0?
Solution:
Given that the equation is
6x – 7y + 8 = 0
7y = 6x + 8
y = 6/7x + 8/7.
Comparing the equation with y = mx + c,
we have m = 6/7 and c = 8/7
Therefore, the slope of the line is 6/7 and y-intercept = 8/7.
Example 5.
What is the slope and y-intercept of the equation 9x – 10y -11 = 0?
Solution:
Given that the equation is
9x – 10y – 11 = 0
10y = 9x – 11
y = 9/10x – 11/10.
Comparing the equation with y = mx + c,
we have m = 9/10 and c = 11/10
Therefore, the slope of the line is 9/10 and y-intercept = 11/10
Example 6.
If the slope of the line joining the points A(x,2) and B(3,6) is 5/4, find the value of x.
Solution:
Given that the two points are
A(x,2) and B(3,6)
x1 = x, y1 = 2, x2 = 3, y2 = 6
Given slope = 5/4
We know that
x2 – x1/y2 – y1
3 – x/6 – 2 = 5/4
3 – x/4 = 5/4
12 – 4x = 20
12 – 20= 4x
-8 = 4x
x = -2
Hence the value of x = -2.
Example 7.
Find the slope of the line joining the points (4,8) and (5,2)
Solution:
Let A(4,8) and B(5,2) be two points.
Slope of the line = y2 – y1/x2 – x1
= 2-8/5 – 4
= -6/1
= -6/1
= -6
Therefore the slope of the given points are 6.
Example 8.
The following points are plotted in x-y plane.Find the slope and y intercept of the line joining each pair of (1,2) & (3,4)
Solution:
Given that the points are (1,2) and (3,4)
x1 = 1, y1 = 2, x2 = 3 and y2 = 4
slope is (y2-y1)/(x2-x1)
(4 – 2)/(3 -1)
= 2/2
Slope =1
then y=mx+c
you get x-y+1=0
at y axis x=0
y = 1
Therefore y-intercept = 1
Example 9.
What is the slope and y-intercept of the equation x – y + 1 = 0?
Solution:
Given that the equation is
x – y + 1 = 0
y = x + 1
Comparing the equation with y = mx + c,
we have m = 1 and c = 1
Therefore, the slope of the line is 1, and y-intercept = 1.
Example 10.
What is the slope and y-intercept of the equation x – 3y – 7 = 0?
Solution:
Given that the equation is
x – 3y – 7 = 0
3y = x – 7
y = 1/3x – 7/3.
Comparing the equation with y = mx + c,
we have m = 1/3 and c = 7/3
Therefore, the slope of the line is 1/3 and y-intercept = 7/3.