Slope-Intercept Form: Real-World Problem Solving

1. A car rental company charges a flat fee of $20 plus $0.15 per mile driven. Write the equation in slope-intercept form and interpret the slope in the context of the problem.

• C = 15 + 0.20m; slope = 0.20 (cost per mile)

• C = 20 + 0.10m; slope = 0.10 (cost per mile)

• C = 25 + 0.15m; slope = 0.15 (cost per mile)

• C = 20 + 0.15m; slope = 0.15 (cost per mile)

2. A local gym charges a monthly membership fee of $30 and an additional $5 per fitness class attended. Create a system of equations to represent the total cost for different numbers of classes and interpret the solution.

• C = 30 + 10x, where C is the total cost and x is the number of classes attended.

• C = 15 + 5x, where C is the total cost and x is the number of classes attended.

• C = 30 - 5x, where C is the total cost and x is the number of classes attended.

• C = 30 + 5x, where C is the total cost and x is the number of classes attended.

4. Two friends are saving money for a concert. Friend A saves $10 a week, while Friend B saves $15 a week. Write a system of equations to represent their savings over time and interpret the point where their savings are equal.

• The system of equations is A = 5x and B = 10x; they are equal at week 5.

• The system of equations is A = 10x and B = 20x; they are equal at week 2.

• The system of equations is A = 10x and B = 15x; they are equal at week 0.

• The system of equations is A = 15x and B = 15x; they are equal at week 1.

5. A phone company offers a plan that costs $40 per month plus $0.10 per text message. Write the equation in slope-intercept form and explain what the y-intercept represents in this scenario.

• y = 0.10x + 40

• y = 40x + 0.10

• y = 40 + 0.10x

• y = 0.10x - 40

6. A farmer sells apples for $2 per pound and oranges for $3 per pound. If the total revenue from selling 50 pounds of fruit is $120, create a system of equations and interpret the solution in the context of the problem.

• 40 pounds of apples and 10 pounds of oranges.

• 10 pounds of apples and 40 pounds of oranges.

• 25 pounds of apples and 25 pounds of oranges.

• The farmer sold 30 pounds of apples and 20 pounds of oranges.

7. A taxi service charges a base fare of $5 plus $2 per mile. Write the equation in slope-intercept form and determine how much a ride of 10 miles would cost.

• $30

• $25

• $15

• $20

8. A bookstore sells novels for $15 each and textbooks for $25 each. If a customer spends $200, create a system of equations to represent the number of novels and textbooks purchased and interpret the solution.

• The system of equations is: 15x + 25y = 200 and x + y = n.

• 10x + 25y = 200 and x + y = 10.

• 15x + 20y = 200 and x + y = 15.

• 15x + 30y = 200 and x + y = 5.

10. A local theater sells tickets for $12 each and popcorn for $5 each. If a family spends $60, create a system of equations to represent the number of tickets and popcorn bags purchased and interpret the solution in context.

• The family can buy 0 tickets and 12 popcorn bags, 1 ticket and 9 popcorn bags, 2 tickets and 6 popcorn bags, 3 tickets and 3 popcorn bags, or 4 tickets and 0 popcorn bags.

• 2 tickets and 10 popcorn bags

• 1 ticket and 5 popcorn bags

• 5 tickets and 0 popcorn bags