A linear model fits a quantity that changes by the same amount each year. Translate “years after” into inputs first: the first year is input , which gives the starting value. Then divide the change in usage by the change in years, using Desmos to read the rate as a fraction. A reduction needs a negative rate; the later amount is not the starting value.
Hints
- Hint 1
The input counts years after 2005, not the calendar year itself. At , what is the water usage? How many years after 2005 is 2018?
- Hint 2
The slope is the change in water usage divided by the change in years. Put later usage minus earlier usage on top. The usage fell, so should the slope be positive or negative?
Step-by-step
Find the starting value and yearly rate
Step 1Turn the years into inputs
The input counts years after 2005, so 2005 is . Count the years to 2018:
The two usage facts become and , in millions of gallons.
- Step 2
Find the yearly rate
The slope is the change in usage for one year. Divide the change in usage by the matching change in years. Type in Desmos. It shows about ; tap its fraction button to see . The negative sign fits a reduction.
- Step 3
Write the model
In slope-intercept form, , the number is the usage at . Here , not : the latter is the usage in 2018. Put in the slope from Desmos:
The model starts at million gallons and decreases by million gallons each year. Choice D.