Slope Calculations and Equation Writing Challenges

A car travels from point A to point B on a straight road. The graph shows the distance in miles on the y-axis and time in hours on the x-axis. If the car travels 120 miles in 3 hours, what is the slope of the line? Write the equation of the line in slope-intercept form.

• Slope: 20 miles per hour; Equation: y = 20x

• Slope: 50 miles per hour; Equation: y = 50x

• Slope: 40 miles per hour; Equation: y = 40x

• Slope: 30 miles per hour; Equation: y = 30x

A gardener is planting flowers in a straight row. The graph shows the number of flowers planted (y) over time in hours (x). If the gardener plants 15 flowers in 2 hours, what is the slope? Write the equation that represents the number of flowers planted over time.

• y = 10x

• y = 5x

• y = 15x

• y = 7.5x

A cyclist rides from point C to point D. The graph indicates the height of the cyclist above sea level (y) versus the distance traveled (x). If the height increases by 50 feet over 5 miles, what is the slope? Write the equation of the line that models this situation.

• Slope: 10 feet per mile; Equation: y = 10x

• Slope: 5 feet per mile; Equation: y = 5x

• Slope: 15 feet per mile; Equation: y = 15x

• Slope: 20 feet per mile; Equation: y = 20x

A student tracks the number of pages read in a book over several days. The table shows the days (x) and pages read (y): Day 1: 10 pages, Day 2: 20 pages, Day 3: 30 pages. Calculate the slope and write the equation for the number of pages read as a function of days.

• y = 15x

• y = 10x

• y = 20x + 10

• y = 5x

A train travels from station X to station Y. The graph shows the speed of the train (y) in miles per hour over time (x) in hours. If the speed increases from 20 mph to 60 mph over 2 hours, what is the slope? Write the equation that represents the speed of the train over time.

• Slope: 30 mph/hour; Equation: y = 30x + 10

• Slope: 25 mph/hour; Equation: y = 25x + 15

• Slope: 15 mph/hour; Equation: y = 15x + 5

• Slope: 20 mph/hour; Equation: y = 20x + 20

A company tracks its sales over the first four months. The table shows the months (x) and sales in thousands (y): Month 1: 5, Month 2: 10, Month 3: 15, Month 4: 20. Calculate the slope and write the equation for sales as a function of months.

• y = 5x

• y = 20x - 5

• y = 10x

• y = 15x + 5

A runner's distance over time is recorded in a graph. If the runner covers 10 miles in 2 hours, what is the slope of the line? Write the equation that represents the distance run over time.

• Slope: 6 miles per hour; Equation: d(t) = 6t

• Slope: 4 miles per hour; Equation: d(t) = 4t

• Slope: 5 miles per hour; Equation: d(t) = 5t

• Slope: 10 miles per hour; Equation: d(t) = 10t

A water tank is being filled at a constant rate. The graph shows the volume of water in gallons (y) over time in minutes (x). If the tank fills from 0 to 100 gallons in 20 minutes, what is the slope? Write the equation for the volume of water as a function of time.

• y = 10x

• y = 5x

• y = 4x

• y = 2.5x

A factory produces widgets, and the graph shows the number of widgets produced (y) over time in hours (x). If the factory produces 200 widgets in 4 hours, what is the slope? Write the equation that models the production of widgets over time.

• y = 50x

• y = 25x

• y = 100x

• y = 75x

A student measures the temperature in a room over several hours. The table shows the hours (x) and temperature in degrees Fahrenheit (y): Hour 1: 68°F, Hour 2: 72°F, Hour 3: 76°F. Calculate the slope and write the equation for temperature as a function of hours.

• y = 2x + 64

• y = 5x + 60

• y = 3x + 70

• y = 4x + 64