Exploring Ratios and Slope in Real-Life Scenarios

A car travels at a constant speed of 60 miles per hour. If the distance traveled is represented by the equation d = 60t, where d is the distance in miles and t is the time in hours, what is the slope of the equation and what does it represent?

• The slope is 60, representing the speed of the car in miles per hour.

• The slope is 90, representing the speed of the car in kilometers per hour.

• The slope is 60, representing the distance traveled in miles.

• The slope is 30, representing the acceleration of the car.

A recipe calls for 2 cups of flour for every 3 cups of sugar. If you want to make a batch with 12 cups of sugar, how many cups of flour will you need?

• 6 cups of flour

• 10 cups of flour

• 8 cups of flour

• 4 cups of flour

A cell phone plan costs $30 per month plus $0.10 per text message. Write an equation to represent the total cost C in terms of the number of text messages x. What is the y-intercept and what does it represent?

• C = 30 + 0.10x; y-intercept = 30, representing the base cost without any text messages.

• C = 0 + 0.10x; y-intercept = 0, representing no monthly fee.

• C = 30 + 0.05x; y-intercept = 0, representing no base cost.

• C = 30x; y-intercept = 0, representing no cost at all.

A school is planning a field trip and has a budget of $500. If each ticket costs $25, how many tickets can they buy? Write an equation to represent this situation and identify the slope.

• 15

• 20

• 30

• 25

A gardener is planting flowers in rows. If each row contains 5 flowers and there are 4 rows, how many flowers are there in total? Write a ratio to represent the relationship between the number of rows and flowers.

• 25 flowers, ratio 1:6

• 10 flowers, ratio 1:2

• 20 flowers, ratio 1:5

• 15 flowers, ratio 1:4

A bike rental shop charges a flat fee of $15 plus $5 for each hour of rental. Write an equation to represent the total cost C in terms of hours h. What does the slope represent in this context?

• C = 5h; the slope represents the total cost of the bike.

• C = 15 + 5h; the slope represents the cost per hour of rental.

• C = 15 + 10h; the slope represents the cost for two bikes.

• C = 15h; the slope represents the initial fee.

A recipe requires 3 eggs for every 4 cups of flour. If you have 12 cups of flour, how many eggs do you need? Write a proportion to solve this problem.

• 9 eggs

• 12 eggs

• 15 eggs

• 6 eggs

A store sells pencils at a rate of 5 for $2. If you want to buy 20 pencils, how much will it cost? Set up a proportion to find the total cost.

• $4

• $6

• $8

• $10

A car can travel 240 miles on 8 gallons of gas. What is the unit rate of miles per gallon? Write an equation to represent the relationship between miles m and gallons g.

• 15 miles per gallon; m = 15g

• 40 miles per gallon; m = 40g

• 20 miles per gallon; m = 20g

• 30 miles per gallon; m = 30g

A painter charges $200 for the first hour and $50 for each additional hour. If you want to hire the painter for 5 hours, how much will it cost? Write an equation to represent the total cost and identify the slope.

• 450

• 250

• 400

• 300