Question

1. airboats you rent an airboat. the total cost includes a flat fee plus an hourly fee. after 4 hours, the total cost is $140.

a) write an equation that represents the total cost y after x hours.
b) interpret the y - intercept.

Explanation:

Step1: Define slope-intercept form

The total cost follows $y = mx + b$, where $m$ = hourly fee, $b$ = flat fee.

Step2: Plug in known values

We know $m=30$, $x=4$, $y=140$. Substitute:
$140 = 30(4) + b$

Step3: Calculate flat fee $b$

$140 = 120 + b$
$b = 140 - 120 = 20$

Step4: Write total cost equation

Substitute $m=30$ and $b=20$ into $y=mx+b$:
$y = 30x + 20$

Step5: Interpret y-intercept

The y-intercept is $b=20$, which occurs at $x=0$ (0 hours rented).

Answer:

a) $y = 30x + 20$
b) The y-intercept of 20 represents the flat, one-time fee to rent the airboat (the cost when renting the airboat for 0 hours, i.e., the base cost before any hourly charges apply).