Practice Questions with Solutions

Q1. Find the slope of the line passing through the points (2, 3) and (5, 11).

Solutions:

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.

Q2. Determine the slope of the line that passes through the points (−4, 7) and (2, −1).

Solutions:

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.

Q3. Write the equation of a line with a slope of 3 and a y-intercept of −2.

Solutions:

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.

Q4. If the equation of a line is y = −4x + 5, what is the slope and y-intercept of this line?

Solutions:

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.

Q5. Write the equation of the line with slope 2 passing through the point (1, 4).

Solutions:

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.

Q6. Given the point (3, −2) and a slope of −1/2, find the equation of the line in point-slope form.

Solutions:

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.

Q7. Convert the equation 3x − 4y = 12 to slope-intercept form and identify the slope and y-intercept.

Solutions:

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

Q8. Find the slope of the line given by the equation 2x + 5y = 10.

Solutions:

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.

Q9. If the slope of a line passing through the points (4, b) and (2, -9) is 3, then what is the value of b?

Solutions:

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.

Q10. Find the slope and y-intercept of the equation of line 2x – y + 5 = 0.

Solutions:

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

The slope of a line indicates its steepness or incline. It shows how much the line rises or falls when moving horizontally from one place to another. In this article, we will learn about slope of line with practice questions and solved examples. We will also look at some formulas and problems of slope of a line.