Exploring Constant Rates: Graphs and Equations in Action

A car travels at a constant speed of 60 miles per hour. If the graph shows the distance traveled over time, what is the slope of the graph?

• 120 miles per hour

• 30 miles per hour

• 90 miles per hour

• 60 miles per hour

A bike rental service charges a flat fee of $10 plus $2 for every hour rented. Write the equation that represents 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 water tank is being filled at a constant rate. The graph shows the volume of water in the tank over time. If the tank reaches 100 liters in 5 hours, what is the rate of change?

• 15 liters per hour

• 20 liters per hour

• 25 liters per hour

• 30 liters per hour

A student is saving money for a new phone. The graph shows her savings over time, and it increases by $15 each week. Write the equation for her savings after 'w' weeks. What does the slope indicate?

• S = 20w; the slope indicates the savings increase by $20 each week.

• S = 15w; the slope indicates the savings increase by $15 each week.

• S = 10w; the slope indicates the savings increase by $10 each week.

• S = 15w + 5; the slope indicates the savings decrease by $15 each week.

A train travels 150 miles in 3 hours. If you were to graph the distance over time, what would be the slope of the line? How does this relate to the train's speed?

• 50 miles per hour

• 30 miles per hour

• 75 miles per hour

• 100 miles per hour

A factory produces 200 widgets in 4 hours. If the production rate is constant, write an equation that represents the number of widgets produced over time. What does the slope of this graph represent?

• W(t) = 200t; the slope represents the total production of 200 widgets.

• W(t) = 100t; the slope represents the production rate of 100 widgets per hour.

• W(t) = 50t; the slope represents the production rate of 50 widgets per hour.

• W(t) = 25t; the slope represents the production rate of 25 widgets per hour.

A gardener plants flowers in a row, and the graph shows the number of flowers planted over time. If he plants 10 flowers every hour, what is the rate of change? Write the equation for the number of flowers after 'h' hours.

• Rate of change: 15 flowers/hour; Equation: F(h) = 15h

• Rate of change: 5 flowers/hour; Equation: F(h) = 5h

• Rate of change: 10 flowers/hour; Equation: F(h) = 10h

• Rate of change: 10 flowers/hour; Equation: F(h) = h + 10

A delivery truck travels a distance of 240 miles in 6 hours. If you were to plot this on a graph, what would be the slope? How can you interpret this slope in terms of speed?

• 40 miles per hour

• 60 miles per hour

• 50 miles per hour

• 30 miles per hour

A student is reading a book and reads 30 pages every day. If the graph shows the number of pages read over time, what is the slope? Write the equation for the total pages read after 'd' days.

• 15, total pages = 15 * d

• 30, total pages = 30 + d

• 45, total pages = 45 * d

• 30, total pages = 30 * d

A swimming pool is being filled at a constant rate of 50 gallons per hour. If the graph shows the total gallons in the pool over time, what is the slope? How would you write an equation for the gallons in the pool after 't' hours?

• The slope is 50; the equation is G(t) = 50t.

• The slope is 50; the equation is G(t) = 50t + 10.

• The slope is 100; the equation is G(t) = 100t.

• The slope is 25; the equation is G(t) = 25t.