Slope and Inequality Challenges in Linear Equations

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write a linear equation to represent the total cost (C) in terms of miles driven (m). What is the slope and y-intercept of this equation?

• Slope: 0.10, Y-intercept: 50

• Slope: 0.20, Y-intercept: 50

• Slope: 0.50, Y-intercept: 20

• Slope: 50, Y-intercept: 0.20

A school is planning a field trip and has a budget of $300. The cost per student is $15. Write an inequality to represent the maximum number of students (s) that can attend the trip. How many students can they afford?

• 15

• 25

• 20

• 30

A gardener is planting flowers in a rectangular garden. The length of the garden is 3 feet more than twice the width. If the width is represented by w, write a linear equation for the length (l). What is the slope of the equation?

• The slope of the equation is 2.

• The slope of the equation is 0.5

• The slope of the equation is 3.

• The slope of the equation is 1.

A local gym charges a monthly fee of $40 plus $5 for each class attended. Write a linear equation to represent the total cost (C) in terms of the number of classes (c). Identify the slope and y-intercept.

• C = 40 + 5c; Slope: 5, Y-intercept: 40

• C = 40 + 2c; Slope: 2, Y-intercept: 40

• C = 40 + 10c; Slope: 10, Y-intercept: 40

• C = 30 + 5c; Slope: 5, Y-intercept: 30

A store is having a sale where the price of a shirt is reduced to $20. If the original price was $30, write an inequality to represent the discount percentage (d) that must be at least 30%. What does this mean for the sale?

• d >= 30%

• d > 50%

• d = 30%

• d < 30%

A delivery service charges a base fee of $10 plus $2 per mile. Write a linear equation for the total cost (C) in terms of miles (m). What is the y-intercept and what does it represent in this context?

• C = 10 + 3m; y-intercept is 10, representing the total cost for 0 miles.

• C = 10 + 5m; y-intercept is 5, representing a discount.

• C = 2m; y-intercept is 0, representing no base fee.

• C = 10 + 2m; y-intercept is 10, representing the base fee.

A student is saving money for a new laptop that costs $800. If they save $50 each week, write an inequality to represent the number of weeks (w) needed to save enough money. How many weeks will it take?

• 16 weeks

• 25 weeks

• 10 weeks

• 20 weeks

A factory produces x toys per hour. The cost to produce these toys is represented by the equation C = 2x + 100. Identify the slope and y-intercept of this equation. What do they represent?

• Slope: 2, Y-intercept: 50

• Slope: 0, Y-intercept: 100

• Slope: 100, Y-intercept: 2

• Slope: 2, Y-intercept: 100

A concert venue has a seating capacity of 500. If tickets are sold for $25 each, write an inequality to represent the total revenue (R) generated from ticket sales. How many tickets need to be sold to reach at least $10,000 in revenue?

• At least 400 tickets need to be sold.

• 300 tickets need to be sold.

• 500 tickets need to be sold.

• 450 tickets need to be sold.

A phone company offers a plan that costs $30 per month plus $0.10 per minute for calls. Write a linear equation to represent the total cost (C) in terms of minutes used (m). What is the slope and what does it indicate about the cost per minute?

• C = 0.10m; Slope = 0.10, indicating no base cost.

• C = 30m + 0.10; Slope = 30, indicating a fixed cost.

• C = 30 + 0.05m; Slope = 0.05, indicating a lower cost per minute.

• C = 30 + 0.10m; Slope = 0.10, indicating the cost per minute.