Slope and Y-Intercept: Real-World Math Challenges

1. A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write the equation for the total cost (C) in terms of miles driven (m). What is the slope and what does it represent in this context?

• C = 50m + 0.20; Slope = 50 (total cost)

• C = 50 + 0.20m; Slope = 0.20 (cost per mile driven)

• C = 0.20 + 50m; Slope = 50 (miles driven)

• C = 50 + 0.50m; Slope = 0.50 (cost per mile driven)

2. The equation of a line representing the temperature (T) in degrees Fahrenheit over time (h) is T = 5h + 32. Identify the slope and explain what it indicates about the temperature change per hour.

• The slope is 10, indicating a temperature increase of 10 degrees Fahrenheit per hour.

• The slope is 5, indicating a temperature increase of 5 degrees Fahrenheit per hour.

• The slope is -5, indicating a temperature decrease of 5 degrees Fahrenheit per hour.

• The slope is 0, indicating no change in temperature over time.

3. A local gym charges a monthly membership fee of $30 plus $10 for each class attended. If you graph the total cost (C) against the number of classes (n), what is the y-intercept and what does it represent?

• 40

• 10

• $30 plus $5 per class

• 30

4. The line representing the distance (d) a cyclist travels over time (t) is given by the equation d = 15t + 5. What is the slope, and what does it tell you about the cyclist's speed?

• The slope is 15, indicating the cyclist's speed is 20 units per time unit.

• The slope is 5, indicating the cyclist's speed is 5 units per time unit.

• The slope is 10, indicating the cyclist's speed is 10 units per time unit.

• The slope is 15, indicating the cyclist's speed is 15 units per time unit.

5. A store sells notebooks for $2 each and charges a $5 service fee. Write the equation for the total cost (C) in terms of the number of notebooks (n). What is the y-intercept and its significance?

• C = 3n + 5; y-intercept = 5, significance: cost when buying three notebooks.

• C = 2n + 10; y-intercept = 10, significance: cost when no notebooks are purchased.

• C = 2n + 0; y-intercept = 0, significance: cost when one notebook is purchased.

• C = 2n + 5; y-intercept = 5, significance: cost when no notebooks are purchased.

6. The graph of a line shows that when the number of hours worked (h) is 0, the earnings (E) are $100. If the slope of the line is $15 per hour, write the equation for earnings in terms of hours worked. What does the slope represent?

• E = 10h + 100; The slope represents the total earnings.

• E = 20h + 50; The slope represents the fixed costs per hour.

• E = 15h - 100; The slope represents the initial investment.

• E = 15h + 100; The slope represents the earnings increase per hour worked.

7. A taxi company charges a base fare of $3 plus $2 per mile. If you were to graph the total fare (F) against the number of miles (m), what is the slope and what does it represent?

• The slope is 3, representing the base fare.

• The slope is 2, representing the cost per mile.

• The slope is 1, representing the total fare.

• The slope is 4, representing the cost per mile.

8. The equation of a line is given as y = -4x + 12. Identify the slope and y-intercept. What do these values indicate about the relationship between x and y?

• Slope: -4, Y-intercept: 12

• Slope: 0, Y-intercept: 12

• Slope: -12, Y-intercept: 4

• Slope: 4, Y-intercept: 12

9. A delivery service charges a flat fee of $10 plus $1.50 for each package delivered. If you were to calculate the y-intercept from a graph of total cost versus number of packages, what would it be and what does it represent?

• $10

• $0

• $15

• $5

10. The equation of a line representing the profit (P) from selling x items is P = 20x - 100. Identify the slope and explain its significance in terms of profit per item sold.

• The slope is 10, indicating a profit of $10 per item sold.

• The slope is 20, representing a profit of $20 per item sold.

• The slope is 0, meaning there is no profit per item sold.

• The slope is 25, representing a profit of $25 per item sold.