﻿ Finding the Slope of a Line Worksheet | Problems & Solutions

Finding the Slope of a Line Worksheet

Finding the Slope of a Line Worksheet
• Page 1
1.
Find the slope of the line that passes through the points (- 3, 4) and (5, 7).
 a. $\frac{3}{8}$ b. $\frac{3}{2}$ c. $\frac{8}{3}$ d. $\frac{2}{11}$

Solution:

m = y2-y1x2-x1
Slope of a line passing through two points, m = Difference between the y-coordinatesDifference between the x-coordinates
[Formula.]

= (7-4)(5-(-3))
[Substitute (x1, y1) = (- 3, 4) and (x2, y2) = (5, 7).]

= 38
[Simplify the fraction.]

The slope of the line passing through the points is 3 / 8.

2.
The slope of the line in the graph is

 a. negative b. positive c. zero d. undefined

Solution:

The line in the graph is rising from left to right.

The line with a positive slope rises from left to right.

So, the slope of the line in the graph is positive.

3.
The slope of the line in the graph is

 a. negative b. positive c. undefined d. zero

Solution:

The line in the graph is falling from left to right.

The line with a negative slope falls from left to right.

So, the slope of the line in the graph is negative.

4.
The slope of the line in the graph is

 a. undefined b. negative c. positive d. zero

Solution:

The line in the graph is horizontal.

Slope = rise / run. The rise in the line is zero.

So, the slope of the line in the graph is zero.

5.
The slope of the line in the graph is

 a. 1 b. undefined c. zero d. - 2

Solution:

The line in the graph is vertical.

Slope = rise / run . The run is zero in the graph.

So, the slope of the line in the graph is undefined.

6.
Find the slope of the line AB in the graph.

 a. - 1 b. 1 c. - 2

Solution:

The coordinates of the point A are (0, 2) and coordinates of the point B are (- 2, 0).

Slope = Change in yChange in x
[Formula.]

= 2 - 00 - (- 2)
[Substitute values.]

= 22 = 1
[Simplify.]

The slope of the line AB is 1.

7.
Find the slope of the line $\stackrel{‾}{\mathrm{AB}}$ in the graph.

 a. 2 b. - 1 c. 1 d. - 2

Solution:

The coordinates of point A are (- 1, 0) and coordinates of point B are (0, - 2).

Slope = Change in yChange in x = - 2 / 1

The slope of the line is - 2.

8.
What is the slope of the diameter AB of the circle shown in the graph?

 a. - 2 b. 1 c. - 1

Solution:

Let A(2, 2) be (x1, y1) and B(- 2, - 2) be (x2, y2).

Let m be the slope of the diameter.

m = y2-y1x2-x1

m = (-2-2)(-2-2)
[Substitute the values of x1, y1, x2 and y2.]

m = 1
[Simplify the fraction.]

The slope of the diameter AB is 1.

9.
Find the slope of the line that passes through the points (13, 14) and (- 15, 17).
 a. $\frac{3}{28}$ b. - $\frac{3}{28}$ c. $\frac{3}{29}$ d. $\frac{4}{29}$

Solution:

m = y2-y1x2-x1
[Slope formula.]

= (17-14)(-15-13)
[Substitute (x1, y1) = (13, 14) and (x2, y2) = (- 15, 17).]

= - 328
[Simplify the fraction.]

The slope of the line passing through the points is - 3 / 28.

10.
Which word describes the slope of a vertical line?
 a. positive b. zero c. negative d. undefined

Solution:

The slope of a line is the ratio of the vertical rise to the horizontal run between any two points on the line.

Slope = Vertical riseHorizonatal run = Change in yChange in x = Change in yzero
[For a vertical line, Change in x is zero.]

The slope of the vertical line is undefined.
[Division by zero is undefined.]