$ \\frac{7 - 3}{6 - 2} = \\frac{4}{4} = 1 $

$ \\frac{6 - 2}{4 - 1} = \\frac{4}{3} $

$ \\frac{y_2 - y_1}{x_2 - x_1} $

Question 1

Given the formula for the slope of a line:

$ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} $

If a line passes through the points $(2, 3)$ and $(6, 7)$, what is the slope of the line?

Accepted Answer

$ \frac{7 - 3}{6 - 2} = \frac{4}{4} = 1 $

Question 2

If the slope of a line is negative, which of the following best describes the direction of the line on a standard Cartesian plane?

Accepted Answer

The line falls as it moves from left to right.

Question 3

A line has a slope of $ \frac{1}{2} $. If the line passes through the point $(2, 1)$, what is the equation of the line in slope-intercept form?

Question 4

Which of the following lines has the steepest slope?

Accepted Answer

A line with a slope of $2$

Question 5

If the slope of a line is $0$, what does the line look like on a graph?

Accepted Answer

It is a horizontal line.

Question 6

Given two points $(1, 2)$ and $(4, 6)$, calculate the slope using the formula $ \frac{y_2 - y_1}{x_2 - x_1} $.

Accepted Answer

$ \frac{6 - 2}{4 - 1} = \frac{4}{3} $

Question 7

If a line passes through the points $(0, 0)$ and $(3, 9)$, what is the slope?

Accepted Answer

$ \frac{9 - 0}{3 - 0} = 3 $

Question 8

Which of the following best represents the meaning of 'rise over run' in the context of the slope of a line?

Accepted Answer

The change in the vertical axis divided by the change in the horizontal axis.

Question 9

A line has a slope of $-1$. If it passes through the point $(2, 4)$, what is the equation of the line in slope-intercept form?

Accepted Answer

$ y = -x + 6 $

Question 10

If the slope of a line is undefined, what does the line look like?

Accepted Answer

It is a vertical line.

Question 11

Suppose a line passes through the points $(5, 2)$ and $(5, 8)$. What is the slope of this line?

Accepted Answer

Undefined

Question 12

If a line has a slope of $0.5$, and you move 4 units to the right along the x-axis, how many units do you move up along the y-axis?

Accepted Answer

2

Question 13

Which of the following is the correct formula for the slope of a line passing through points $(x_1, y_1)$ and $(x_2, y_2)$?

Accepted Answer

$ \frac{y_2 - y_1}{x_2 - x_1} $

Question 14

A line passes through $(1, 1)$ and $(3, 5)$. What is the slope?

Accepted Answer

$ \frac{5 - 1}{3 - 1} = 2 $

Question 15

If a line has a slope of $1$, which of the following points does NOT lie on the line $y = x + 2$?

Accepted Answer

$(3, 5)$

Question 16

If the slope of a line is $0$, and it passes through the point $(4, 7)$, what is the equation of the line?

Accepted Answer

$ y = 7 $

Understanding the Slope of Linear Graphs

Study Guide - Practice Questions