Mastering Linear Equations: Slope & Intercept Insights

1. A taxi company charges a base fare of $3 plus $2 per mile. Write a linear equation to represent the total cost (C) of a ride based on the number of miles (m) traveled. What is the slope and what does it represent?

• C = 3 + 2m; Slope = 2 (cost per mile)

• C = 3 + 3m; Slope = 3 (cost per mile)

• C = 5 + 2m; Slope = 2 (total cost)

• C = 2 + 3m; Slope = 3 (base fare)

2. A cell phone plan costs $30 per month plus $0.10 for each text message sent. Write the linear equation for the total cost (C) based on the number of text messages (t). What does the y-intercept represent in this context?

• C = 30 + 0.05t; y-intercept represents the annual fee of $30.

• C = 30 + 0.10t; y-intercept represents the monthly fee of $30.

• C = 0.10t; y-intercept represents the cost per text message.

• C = 30t + 0.10; y-intercept represents the total cost of texts.

3. A gardener charges a flat fee of $50 to start a landscaping project and $25 for each hour of work. Write the equation for the total cost (C) based on hours worked (h). How would you interpret the slope?

• C = 50 + 50h

• C = 25 + 50h

• C = 50h + 25

• C = 50 + 25h

4. A car rental company charges a daily fee of $40 plus $0.15 per mile driven. Write the equation for the total cost (C) based on miles driven (m). What does the slope indicate about the cost per mile?

• C = 30 + 0.15m; the slope indicates the cost per mile is $0.15.

• C = 40 + 0.15m; the slope indicates the cost per mile is $0.15.

• C = 40 + 0.20m; the slope indicates the cost per mile is $0.20.

• C = 40 + 0.10m; the slope indicates the cost per mile is $0.10.

5. A gym membership costs $20 per month plus a one-time registration fee of $50. Write the linear equation for the total cost (C) based on the number of months (m). What does the y-intercept represent?

• C = 50m + 20; y-intercept represents the monthly cost of $20.

• C = 20m; y-intercept represents the total cost after one month.

• C = 20m + 50; y-intercept represents the registration fee of $50.

• C = 50 + 20m; y-intercept represents the total cost for zero months.

6. A delivery service charges a flat fee of $10 plus $5 for each package delivered. Write the equation for the total cost (C) based on the number of packages (p). What does the slope tell you about the cost per package?

• C = 10 + 10p; The slope of 10 indicates the cost per package is $10.

• C = 10 + 5p; The slope of 5 indicates the cost per package is $5.

• C = 10 + 2p; The slope of 2 indicates the cost per package is $2.

• C = 5 + 10p; The slope of 10 indicates the cost per package is $10.

7. A school is selling tickets for a play at $8 each. If they also have a fixed cost of $200 for the venue, write the equation for total revenue (R) based on the number of tickets sold (t). What does the slope represent?

• R = 8t - 200; slope = 8

• R = 8t + 200; slope = 8

• R = 10t - 200; slope = 10

• R = 5t - 200; slope = 5

8. A water company charges a monthly fee of $15 plus $2 for every 100 gallons used. Write the equation for the total bill (B) based on gallons used (g). How would you interpret the slope?

• B = 15 + 0.02g^2

• B = 15 + 2g

• B = 15 + 0.02g

• B = 15 + 0.5g

9. A subscription service charges $10 per month plus a one-time setup fee of $25. Write the equation for the total cost (C) based on the number of months (m). What does the y-intercept indicate?

• C = 10m - 25; y-intercept indicates the monthly fee of $10.

• C = 10m + 10; y-intercept indicates the total cost without any fees.

• C = 10m + 25; y-intercept indicates the initial setup fee of $25.

• C = 25m + 10; y-intercept indicates the total cost after one month.

10. A local farmer sells apples for $2 each and has a fixed cost of $50 for supplies. Write the equation for total revenue (R) based on the number of apples sold (a). What does the slope represent in this scenario?

• R = 2a; the slope represents the revenue per apple sold.

• R = 2a - 50; the slope represents the profit per apple sold.

• R = 50 + 2a; the slope represents the total cost of supplies.

• R = 2a + 50; the slope represents the fixed cost of supplies.