Understanding Slope: Real-World Linear Equations Quiz

A car travels at a constant speed of 60 miles per hour. Write the equation that represents the distance traveled over time. What is the slope of this equation and what does it represent in this context?

• d = 60t; slope = 120 miles per hour

• d = 30t; slope = 30 miles per hour

• d = 60t + 10; slope = 60 miles per hour

• d = 60t; slope = 60 miles per hour

A bike rental shop charges a flat fee of $10 plus $2 for every hour the bike is rented. Write the equation for the total cost based on the number of hours rented. What does the slope represent?

• C = 10 + 2h; the slope represents the cost per hour of renting the bike.

• C = 10 + 3h; the slope represents the discount per hour of renting the bike.

• C = 10 + 5h; the slope represents the total cost of renting the bike.

• C = 5 + 2h; the slope represents the initial fee for renting the bike.

A gardener plants a tree that grows 3 inches every month. If the tree is currently 24 inches tall, write an equation to represent its height over time. What does the slope indicate?

• h(t) = 24 - 3t; the slope indicates the tree shrinks 3 inches per month.

• h(t) = 24 + 5t; the slope indicates the tree grows 5 inches per month.

• h(t) = 24 + 2t; the slope indicates the tree grows 2 inches per month.

• h(t) = 24 + 3t; the slope indicates the tree grows 3 inches per month.

A student scores 80 points on a test and improves by 5 points for each subsequent test. Write the equation for the student's score over time. What does the slope represent in this scenario?

• S(t) = 80 + 5t; the slope is 5.

• S(t) = 80 + 10t; the slope is 10.

• S(t) = 85 + 5t; the slope is 5.

• S(t) = 80 - 5t; the slope is -5.

A delivery truck travels 150 miles in 3 hours. Write the equation that represents the relationship between distance and time. What is the slope and what does it signify?

• d = 50t; slope = 50, signifies speed in miles per hour.

• d = 150t; slope = 150, signifies time in hours.

• d = 50t; slope = 25, signifies average speed in kilometers per hour.

• d = 75t; slope = 75, signifies total distance traveled.

A factory produces 200 toys in 4 hours. Write an equation to represent the production rate. What does the slope of this equation tell you about the factory's output?

• The equation is y = 200x, and the slope indicates the factory produces 200 toys per hour.

• The equation is y = 50x, and the slope indicates the factory produces 50 toys per hour.

• The equation is y = 25x, and the slope indicates the factory produces 25 toys per hour.

• The equation is y = 100x, and the slope indicates the factory produces 100 toys per hour.

A swimming pool is filled at a rate of 10 gallons per minute. If it starts with 500 gallons, write the equation for the total gallons in the pool over time. What does the slope represent?

• G(t) = 10t; the slope represents the initial amount of water.

• G(t) = 500 - 10t; the slope represents the decrease in water level.

• G(t) = 500 + 5t; the slope represents the filling rate of 5 gallons per minute.

• G(t) = 500 + 10t; the slope represents the filling rate of 10 gallons per minute.

A restaurant serves 50 customers in the first hour and increases by 10 customers each hour. Write the equation for the number of customers served over time. What does the slope indicate?

• y = 50 - 10x; slope = -10 (10 fewer customers each hour)

• y = 40 + 5x; slope = 5 (5 more customers each hour)

• y = 50 + 10x; slope = 10 (10 more customers each hour)

• y = 60 + 10x; slope = 10 (10 more customers each hour)

A train travels 120 miles in 2 hours. Write the equation that represents the train's speed. What does the slope of this equation represent in real-world terms?

• y = 30x; the slope represents the train's speed of 30 miles per hour.

• y = 60x; the slope represents the train's speed of 60 miles per hour.

• y = 60x + 10; the slope represents the train's speed of 70 miles per hour.

• y = 120x; the slope represents the train's speed of 120 miles per hour.

A phone plan costs $30 per month plus $0.10 per text message. Write the equation for the total cost based on the number of messages sent. What does the slope represent in this context?

• C = 30 + 0.20m; the slope represents the number of messages sent.

• C = 30m + 0.10; the slope represents the fixed cost of the plan.

• C = 30 + 0.10m; the slope (0.10) represents the cost per text message.

• C = 30 + 0.05m; the slope represents the total monthly cost.