Exploring Negative Slopes: Write and Interpret Equations

A car is traveling down a hill that has a slope of -3. If the car starts at a height of 150 meters, write the equation in slope-intercept form that represents the height of the car as it travels down the hill.

• y = 3x + 150

• y = -3x + 100

• y = -3x - 150

• y = -3x + 150

A delivery truck is descending a ramp that decreases in height by 2 meters for every 5 meters it travels horizontally. Write the equation in slope-intercept form for the height of the truck as it moves along the ramp.

• h = -\frac{2}{5}x + b

• h = -2x + b

• h = rac{2}{5}x + b

• h = -rac{5}{2}x + b

The temperature in a city drops by 4 degrees every hour after sunset. If the temperature at sunset is 20 degrees, write the equation in slope-intercept form to represent the temperature over time after sunset.

• T = 20 + 4t

• T = 20 - 4t

• T = 16 - 4t

• T = 20 - 2t

A cyclist is riding downhill, and for every 1 mile traveled, the elevation decreases by 100 feet. If the starting elevation is 800 feet, write the equation in slope-intercept form for the cyclist's elevation as a function of distance traveled.

• y = -200x + 800

• y = -50x + 800

• y = -100x + 1000

• y = -100x + 800

A company's profit decreases by $500 for every 10 units sold. If the initial profit is $5,000, write the equation in slope-intercept form to represent the profit based on the number of units sold.

• P = -50x + 4000

• P = -50x + 5000

• P = -100x + 6000

• P = 50x + 5000

A student is tracking her savings, which decrease by $15 each week due to expenses. If she starts with $200, write the equation in slope-intercept form to represent her savings over time.

• y = 15x + 200

• y = -10x + 200

• y = -15x + 200

• y = -15x + 150

A water tank is leaking at a rate of 3 liters per hour. If the tank initially holds 120 liters, write the equation in slope-intercept form to represent the amount of water left in the tank over time.

• y = 3t + 120

• y = -3t + 100

• y = -5t + 120

• y = -3t + 120

A hiker is going down a mountain that has a slope of -1.5. If the hiker starts at an elevation of 1,200 meters, write the equation in slope-intercept form for the hiker's elevation as they descend.

• y = -1.5x + 1000

• y = -1.5x - 1200

• y = 1.5x + 1200

• y = -1.5x + 1200

A stock's value decreases by $2 for every day that passes. If the stock is currently valued at $50, write the equation in slope-intercept form to represent the stock's value over time.

• y = -2x + 50

• y = 50 - 2x

• y = -2x - 50

• y = 2x + 50

A farmer's crop yield decreases by 10 bushels for every acre of land that is not irrigated. If the initial yield is 200 bushels, write the equation in slope-intercept form to represent the yield based on the acres not irrigated.

• y = 200 - 10x

• y = 200 + 10x

• y = 200 - 5x

• y = 190 - 10x