Question

the graph shows the charges of an instructor. the instructor charges an initial fee and then an hourly rate of $8.00 an hour for private lessons. determine the instructors initial charge from the graph. $

Explanation:

Step1: Define linear cost model

Let $y$ = total cost, $x$ = hours, $b$ = initial charge. The model is $y = 8x + b$.

Step2: Substitute a point into model

Use point $(4, 52)$:
$52 = 8(4) + b$

Step3: Calculate initial charge

First compute $8(4)=32$, then solve for $b$:
$b = 52 - 32 = 20$
Verify with another point (e.g., $(5,60)$): $8(5)+20=40+20=60$, which matches.

Answer:

$\boldsymbol{20}$