Exploring Linear Equations: Rates & Line Relationships

A car travels at a constant speed of 60 miles per hour. Write a linear equation to represent the distance traveled over time. What is the rate of change in this scenario?

• d = 60t; Rate of change = 60 miles per hour

• d = 60t + 10; Rate of change = 70 miles per hour

• d = 30t; Rate of change = 30 miles per hour

• d = 60t; Rate of change = 50 miles per hour

A store sells apples for $2 each and bananas for $1 each. If you buy x apples and y bananas, write a linear equation for the total cost. What is the rate of change of cost with respect to the number of apples?

• 2

• $2.50

• 1

• 3

A bike rental shop charges a flat fee of $10 plus $5 per hour. Write a linear equation for the total cost of renting a bike for h hours. What is the rate of change?

• C = 10 + 7h; Rate of change = 7

• C = 10 + 5h; Rate of change = 5

• C = 15 + 5h; Rate of change = 5

• C = 10 + 3h; Rate of change = 3

A gardener is planting two types of flowers. The first type grows at a rate of 2 inches per week, and the second type grows at 3 inches per week. Write equations for their heights over time. Are the growth rates parallel or perpendicular?

• The growth rates are perpendicular.

• The growth rates are equal.

• The growth rates are parallel.

• The growth rates are neither parallel nor perpendicular.

A train travels from City A to City B at a speed of 80 miles per hour. Write a linear equation for the distance from City A over time. If another train travels at 60 miles per hour, how do their rates of change compare?

• The linear equation for the first train is d = 80t; the second train's equation is d = 60t. The first train is faster.

• The first train is slower than the second train.

• Both trains travel at the same speed of 80 miles per hour.

• The first train's equation is d = 60t; the second train's equation is d = 80t.

A delivery truck travels 50 miles in 1 hour and 75 miles in 1.5 hours. Write a linear equation for the distance over time. What is the rate of change, and is it consistent?

• The linear equation is d = 75t, with a rate of change of 75 miles/hour.

• The linear equation is d = 25t, with a consistent rate of change of 25 miles/hour.

• The linear equation is d = 50t, with a consistent rate of change of 50 miles/hour.

• The linear equation is d = 50t + 25, with a rate of change of 50 miles/hour.

A swimming pool is being filled at a rate of 10 gallons per minute. Write a linear equation for the volume of water in the pool over time. What is the rate of change?

• V(t) = 5t; Rate of change = 5 gallons per minute

• V(t) = 10t + 20; Rate of change = 20 gallons per minute

• V(t) = 15t; Rate of change = 15 gallons per minute

• V(t) = 10t; Rate of change = 10 gallons per minute

A school is planning a field trip. The cost per student is $15, and there are 20 students. Write a linear equation for the total cost. What is the rate of change with respect to the number of students?

• C = 15n + 5; Rate of change = $5 per student

• C = 20n; Rate of change = $20 per student

• C = 15 + n; Rate of change = $15 total

• C = 15n; Rate of change = $15 per student

A factory produces 100 toys in 2 hours and 150 toys in 3 hours. Write a linear equation for the number of toys produced over time. What is the rate of change, and is it constant?

• y = 100x, rate of change = 100, not constant

• y = 75x, rate of change = 75, constant

• y = 25x, rate of change = 25, constant

• y = 50x, rate of change = 50, constant