Slope and Equations: Solving Linear Word Problems

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).

• C = 50 + 0.20m

• C = 0.20m - 50

• C = 50 + 0.50m

• C = 50 - 0.20m

The graph shows the relationship between the number of hours worked and the total pay earned. If the slope of the line is 15, what does this slope represent in the context of the problem?

• The slope represents the hourly wage, which is 15 currency units per hour.

• The slope represents the total pay earned after 10 hours.

• The slope shows the total earnings for a fixed number of hours.

• The slope indicates the number of hours worked per currency unit.

A gardener plants flowers in a straight line. The graph shows that for every 2 feet of length, he plants 3 flowers. What is the slope of the line, and what does it represent?

• 2 flowers per foot

• 1 flower per foot

• 1.5 flowers per foot

• 3 flowers per foot

A school is selling tickets for a play. The cost of tickets is $10 each, and the total revenue can be represented by a linear equation. Write the equation for total revenue (R) based on the number of tickets sold (t).

• R = 10t

• R = 20t

• R = 10 + t

• R = 5t

A bike shop sells bikes for $200 each. If the shop sells 5 bikes, the total revenue is represented by a point on a graph. What is the slope of the line representing revenue as a function of the number of bikes sold?

• 150

• 100

• 200

• 250

A train travels at a constant speed. The graph shows the distance traveled over time. If the slope of the line is 60 miles per hour, what does this tell you about the train's speed?

• The train's speed is variable and changes over time.

• The train's speed is 60 miles per hour.

• The train's speed is 90 miles per hour.

• The train's speed is 30 miles per hour.

A local bakery sells cupcakes for $3 each. If the bakery sells 10 cupcakes, what is the equation that represents the total sales (S) based on the number of cupcakes sold (c)?

• S = 10c

• S = c + 3

• S = 30

• S = 3c

The graph shows the relationship between the number of hours studied and test scores. If the slope of the line is 5, what does this indicate about the relationship between studying and test scores?

• The slope of 5 means studying has no effect on test scores.

• Each hour studied decreases test scores by 5 points.

• The slope indicates a negative relationship between studying and test scores.

• The slope of 5 indicates that each hour studied increases test scores by 5 points.

A phone company charges a monthly fee of $30 plus $0.10 per text message. Write an equation to represent the total bill (B) as a function of the number of text messages (t).

• B = 30 + 0.05t

• B = 0.10 + 30t

• B = 30 + 0.10t

• B = 30t + 0.10

A fitness center charges a membership fee of $25 plus $5 per class attended. If a member attends 8 classes, what is the total cost, and what is the slope of the line representing cost as a function of classes attended?

• Total cost: $75, Slope: $2

• Total cost: $80, Slope: $0

• Total cost: $65, Slope: $5

• Total cost: $50, Slope: $10