Two time-and-cost pairs give two points on a linear model. The slope is the change in dollars divided by the change in hours; the intercept is the cost at zero hours. Put the pairs in a Desmos table and fit a line, then convert the fitted decimals to fractions. Don't treat the first listed cost as the intercept unless its time is zero.
Hints
- Hint 1
A point pairs an input with its output. Here, hours are the first coordinate and cost is the second. How can you write each rental fact as a point ?
- Hint 2
The slope is the dollar increase for one extra hour, not a total cost divided by its hours. Fit both points in a Desmos table so the same line has to match both costs.
- Hint 3
The intercept is the cost the model gives at hours. Once Desmos fits the line, type each fitted number on its own line to reveal the fractions used in the choices.
Step-by-step
Fit a line through the two costs
Step 1Turn the rental facts into points
The input is hours and the output is cost, so $25 for 6 hours means , giving . Likewise, $47 for 14 hours gives . Keep hours first in each point.
- Step 2
Find the hourly rate and starting cost
Enter those points in a Desmos table, then type . The tells Desmos to fit one line to both rows. Under PARAMETERS, it shows and . The slope is dollars per hour; the intercept is the cost at hours. The intercept is not the first listed cost unless its time is .
- Step 3
Write the cost equation
Type and on separate lines and tap each line's fraction button. Desmos gives and . In , the first number is the per-hour charge and the second is the fixed cost, so . Choice A.