Slope and Rate of Change Worksheet

Question 1

A line passes through the points (2, 3) and (6, 11). Find the slope of the line.

Accepted Answer

The slope of the line is 2 because the change in y is 11 - 3 = 8 and the change in x is 6 - 2 = 4, so the slope is 8/4 = 2.

Question 2

Find the slope of the line that passes through the points (-1, 4) and (3, 0).

Accepted Answer

The slope of the line is -1 because the change in y is 0 - 4 = -4 and the change in x is 3 - (-1) = 4, so the slope is -4/4 = -1.

Question 3

A car travels 120 miles in 3 hours at a constant rate. What is the rate of change in miles per hour?

Accepted Answer

The rate of change is 40 miles per hour because 120 divided by 3 equals 40.

Question 4

The table shows a relationship between x and y values: x = 1, 2, 3, 4 and y = 5, 8, 11, 14. Find the slope or rate of change.

Accepted Answer

The slope is 3 because each time x increases by 1, y increases by 3.

Question 5

The points (4, 7) and (4, 12) lie on the same line. What can you say about the slope?

Accepted Answer

The slope is undefined because the change in x is 4 - 4 = 0, and division by zero is not possible.

Question 6

The temperature changes from 18 degrees to 6 degrees over 4 hours. Find the rate of change in degrees per hour.

Accepted Answer

The rate of change is -3 degrees per hour because the temperature changed by 6 - 18 = -12 degrees over 4 hours, and -12 divided by 4 equals -3.

Question 7

A line has a slope of 5. Explain what this means in terms of rise and run.

Accepted Answer

A slope of 5 means the line rises 5 units for every 1 unit it moves to the right.

Question 8

Find the slope of the line through the points (0, -2) and (5, 8).

Accepted Answer

The slope of the line is 2 because the change in y is 8 - (-2) = 10 and the change in x is 5 - 0 = 5, so the slope is 10/5 = 2.

Question 9

A plant grows from 10 centimeters to 22 centimeters in 6 days. What is the rate of change in centimeters per day?

Accepted Answer

The rate of change is 2 centimeters per day because the plant grew 22 - 10 = 12 centimeters in 6 days, and 12 divided by 6 equals 2.

Question 10

The table shows x = 0, 2, 4, 6 and y = 1, 5, 9, 13. Find the slope.

Accepted Answer

The slope is 2 because y increases by 4 while x increases by 2, and 4 divided by 2 equals 2.

Question 11

Find the slope of the line through the points (-3, -1) and (1, 7).

Accepted Answer

The slope of the line is 2 because the change in y is 7 - (-1) = 8 and the change in x is 1 - (-3) = 4, so the slope is 8/4 = 2.

Question 12

A savings account balance goes from 90 dollars to 150 dollars in 5 weeks. What is the rate of change in dollars per week?

Accepted Answer

The rate of change is 12 dollars per week because the balance increased by 150 - 90 = 60 dollars in 5 weeks, and 60 divided by 5 equals 12.

Question 13

A line has slope 0. Describe what the graph of this line looks like.

Accepted Answer

A line with slope 0 is a horizontal line because the y-value stays the same while x changes.

Question 14

Compare the slopes of these two situations: Line A rises 4 units for every 2 units to the right. Line B rises 3 units for every 1 unit to the right. Which line has the greater slope?

Accepted Answer

Line B has the greater slope because Line A has slope 4/2 = 2 and Line B has slope 3/1 = 3, and 3 is greater than 2.

Question 15

A biker rides 15 miles in 1 hour, then 30 miles in 2 hours, then 45 miles in 3 hours. Is the rate of change constant? If so, what is it?

Accepted Answer

Yes, the rate of change is constant. The biker travels 15 miles each hour, so the rate of change is 15 miles per hour.

Slope and Rate of Change

Slope and Rate of Change

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