Practice Questions on Slope of a line (original) (raw)
Last Updated : 22 Jan, 2026
The slope of a line describes how steep a line is and the direction in which it tilts on a coordinate plane. It tells us how much the y-value (vertical change) changes for a given change in the x-value (horizontal change).
Solved Practice Questions
**1. Find the slope of the line passing through the points (2, 3) and (5, 11).
Given points are (2, 3) and (5, 11)
So, to find the slope when two points are given, use the following formula
m = (y2 - y1)/(x2 - x1)
m = (11 - 3)/(5 - 2)
m = 8/3
So, the slope of the line passing through the points (2, 3) and (5, 11) is 8/3.
**2. Determine the slope of the line that passes through the points (−4, 7) and (2, −1).
Given points are (-4, 7) and (2, -1)
So, to find the slope when two points are given, use the following formula
m = (y2 - y1)/(x2 - x1)
m = (-1 - 7)/(2 - -4)
m = (-8)/6
m = -4/3
So, the slope of the line passing through the points (-4, 7) and (2, -1) is -4/3.
**3. Write the equation of a line with a slope of 3 and a y-intercept of −2.
Given slope = 3 and y-intercept is -2
So, to write the equation of a line when slope and y-intercept is given, use the following formula
y = mx + b
y = 3x - 2
So, the equation of the line with slope 3 and y-intercept of -2 is y = 3x - 2.
4****. If the equation of a line is y = −4x + 5, what is the slope and y-intercept of this line?**
Given equation of line is y = -4x + 5
So, to find the slope when equation of a line is given,, use the following formula
y = mx + b
y = -4x + 5
So, slope = -4 and y-intercept = 5
So, the slope of the line and y-intercept is -4 and 5 respectively.
**5. Write the equation of the line with slope 2 passing through the point (1, 4).
Given slope = 2 and point is (1, 4)
So, to find the equation of line when slope and point is given, use the following formula
y - y1 = m(x - x1)
y - 4 = 2(x - 1)
y - 4 = 2x - 2
y = 2x + 2
So, the equation of the line is y = 2x + 2.
6****. Given the point (3, −2) and a slope of −1/2, find the equation of the line in point-slope form.**
Given slope = -1/2 and point is (3, -2)
So, to find the equation of line when slope and point is given, use the following formula
y - y1 = m(x - x1)
y - (-2) = (-1/2)(x - 3)
2(y + 2) = -x + 3
2y + 4 = -x + 3
y = -x/2 - 1/2.
So, the equation of the line is y = -x/2 - 1/2.
7. C**onvert the equation 3x − 4y = 12 to slope-intercept form and identify the slope and y-intercept.
Given equation of line is 3x - 4y = 12
So, to find the slope of line and y-intercept, convert it into slope-intercept form
y = mx + b
4y = 3x - 12
y = 3x/4 - 3
so, slope = 3/4 and y-intercept = -3
So, the slope is 3/4 and y-intercept is -3
8. Fi**nd the slope of the line given by the equation 2x + 5y = 10.
Given equation of line is 2x + 5y = 10
So, to find the slope of line and y-intercept, convert it into slope-intercept form
y = mx + b
2x + 5y = 10
y = -2x/5 + 2
so, slope = -2/5 and y-intercept = 2
So, the slope is -2/5 and y-intercept is 2.
9. I**f the slope of a line passing through the points (4, b) and (2, -9) is 3, then what is the value of b?
Given,
Slope = m = 3
Points:
(x1 , y1 ) = (4, b)
(x2, y2) = (2, -9)
We know that,
Slope (m) = (y2– y1 )/(x2– x1)
3 = (-9 – b)/(2 – 4)
3 = (-9 – b)/(-2)
-9 – b = 3(-2)
-9 – b = -6
b = -9 + 6 = -3
Therefore, the value of b = -3.
10. **Find the slope and y-intercept of the equation of line 2x – y + 5 = 0.
Given equation of a line:
2x – y + 5 = 0
First we will convert it into slope form
y = 2x + 5
This is of the form y = mx + b
Here, m = 2 and b = 5
Therefore, slope = 2 and y-intercept = 5
Also Check
Practice Questions on Slope of a Line - Unsolved
Q1. Find the slope of the line passing through the points (1, −2) and (4, 8).
Q2. Determine the slope of the line that passes through the points (−3, 5) and (3, −7).
Q3. Write the equation of a line with a slope of −2 and a y-intercept of 4.
Q4. If the equation of a line is y = 1/2x - 3, what is the slope and y-intercept of this line?
Q5. Write the equation of the line with slope 4 passing through the point (2, −3).
Q6. Given the point (5, 1) and a slope of 2/3 , find the equation of the line in point-slope form.
Q7. Convert the equation 4x − 6y = 18 to slope-intercept form and identify the slope and y-intercept.
Q8. Find the slope of the line given by the equation 3x + 4y = 12.
Q9. What is the slope of the line with the equation x = 5? Is it vertical or horizontal?
Q10. Determine the slope of the line represented by y = −6. Is this line vertical or horizontal?
Answer Key
**Q1. 10/3
**Q2. −2
**Q3. y = −2x + 4
**Q4. Slope: 1/2, y-intercept: −3
**Q5. y = 4x − 11
**Q6. y − 1 = 2/3(x − 5)
**Q7. y = (2/3)x − 3, slope: 2/3, y-intercept: −3
**Q8. −3/4
**Q9. Undefined, vertical
**Q10. 0, horizontal