Mastering Slope: Real-World Linear Equation Challenges

A car rental company charges a flat fee of $20 plus $0.15 per mile driven. Write the equation for the total cost (C) in terms of miles driven (m). What is the slope and y-intercept?

• C = 20 + 0.20m; Slope: 0.20, Y-intercept: 20

• C = 15 + 0.15m; Slope: 0.15, Y-intercept: 15

• C = 20 + 0.10m; Slope: 0.10, Y-intercept: 20

• C = 20 + 0.15m; Slope: 0.15, Y-intercept: 20

If a line has a slope of 3 and passes through the point (2, 5), what is the equation of the line in slope-intercept form?

• y = 3x - 5

• y = 3x - 1

• y = -3x + 11

• y = 3x + 5

A gardener is planting flowers in a straight line. If the first flower is planted at 2 feet and each subsequent flower is planted 1.5 feet apart, write the equation for the position of the nth flower. What is the slope?

• position(n) = 1.5n + 0.5; slope = 1.5

• position(n) = 1.5n + 1; slope = 1.5

• position(n) = 1.5n + 2; slope = 1

• position(n) = 2n + 0.5; slope = 2

A school is planning a fundraiser. They sell tickets for $10 each and have a fixed cost of $200. Write the equation for the total revenue (R) in terms of the number of tickets sold (t). What is the slope?

• R = 5t; slope = 5

• R = 200 + 10t; slope = 200

• R = 10t; slope = 10

• R = 10t - 200; slope = -10

A bike rental shop charges a base fee of $5 and $2 for each hour rented. Write the equation for the total cost (C) in terms of hours rented (h). What does the slope represent in this context?

• C = 5 + 2h; the slope represents the cost per hour of renting the bike.

• C = 5 + 3h; the slope represents the discount per hour of renting the bike.

• C = 5h + 2; the slope represents the base fee of renting the bike.

• C = 2h; the slope represents the total cost of the bike.

A train travels at a constant speed of 60 miles per hour. If it starts from a station at 0 miles after 0 hours, write the equation for the distance (d) in terms of time (t). What is the slope of this line?

• d = 60t; slope = 30

• d = 60t; slope = 60

• d = 30t; slope = 30

• d = 60t + 10; slope = 60

A local gym charges a monthly membership fee of $30 plus $5 for each class attended. Write the equation for the total cost (C) in terms of classes attended (c). What is the y-intercept?

• 30

• 35

• 25

• 40

A delivery service charges a flat rate of $15 plus $0.50 per mile. If a customer wants to know the total cost for 10 miles, how would you calculate it using the equation? What is the slope?

• $15

• $25

• $10

• $20

A student is saving money for a new laptop. If they save $50 each month starting with $100, write the equation for the total savings (S) in terms of months (m). What is the slope and what does it represent?

• S = 50m; slope = 100, representing initial savings.

• S = 100 + 25m; slope = 25, representing bi-monthly savings.

• S = 100 - 50m; slope = -50, representing monthly expenses.

• S = 100 + 50m; slope = 50, representing monthly savings.

A phone company offers a plan that costs $40 per month plus $0.10 per text message. Write the equation for the total cost (C) in terms of the number of text messages (t). What is the y-intercept and what does it represent?

• C = 40 + 0.10t; y-intercept = 40, representing the base cost of the plan.

• C = 30 + 0.10t; y-intercept = 30, representing a discount on the plan.

• C = 40t; y-intercept = 0, representing no cost for texts.

• C = 40 + 0.05t; y-intercept = 0, representing no base cost.