Exploring Linear Relationships and Slope Calculation

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write an equation to represent the total cost (C) as a function of miles driven (m). What is the slope of this line?

• 0.20

• $0.20 per hour

• $50

• 0.50

A school is tracking the number of students participating in after-school activities over the years. In 2018, there were 100 students, and in 2022, there were 160 students. What is the slope of the line that represents this relationship?

• 40

• 20

• 30

• 15

A gardener is planting flowers in a rectangular garden. The length of the garden is 3 times its width. If the width is represented by w, write an equation for the length and identify the linear relationship.

• L = 3w

• L = 4w

• L = w + 3

• L = 2w

A local gym tracks the number of memberships sold each month. In January, they sold 30 memberships, and by June, they sold 90. What is the slope of the line that represents the increase in memberships?

• 15

• 12

• 25

• 20

A bike shop sells bikes for $200 each and offers a discount of $20 for every bike purchased. Write an equation for the total cost (C) based on the number of bikes (b) purchased and calculate the slope.

• C = 220b; slope = 220

• C = 160b; slope = 160

• C = 180b; slope = 180

• C = 200b; slope = 200

A student measures the height of a plant every week. After 4 weeks, the plant is 12 inches tall. After 8 weeks, it is 24 inches tall. What is the slope of the line that represents the height of the plant over time?

• 3 inches per week

• 4 inches per week

• 2 inches per week

• 1 inch per week

A city is planning to build a new park. They estimate that the cost will increase linearly from $100,000 in the first year to $300,000 in the third year. What is the slope of the cost over these years?

• 200000

• 150000

• 250000

• 100000

A bookstore tracks the number of books sold each month. In March, they sold 150 books, and in July, they sold 300 books. What is the slope of the line that represents the sales over these months?

• 300

• 75

• 150

• 37.5

A factory produces 500 toys in the first month and increases production by 100 toys each subsequent month. Write an equation for the number of toys produced (T) as a function of months (m) and identify the slope.

• T = 600 + 100m; slope = 100

• T = 500 + 100m; slope = 100

• T = 500 + 50m; slope = 50

• T = 500 + 200m; slope = 200

A student is saving money for a new laptop. They save $50 each month. If they start with $100, write an equation for the total savings (S) as a function of months (m) and calculate the slope.

• S = 100 - 50m; slope = -50

• S = 100 + 25m; slope = 25

• S = 100 + 50m; slope = 50

• S = 50m; slope = 100