Question

in the table below, justin records the number of hours his mechanic works and the total charge. the data can be modeled with a linear function. which statement is true? o a. the mechanic charges $35 per hour. o b. the mechanic charges $40 per hour. o c. the mechanic charges a $20 flat fee, plus $25 per hour. o d. the mechanic charges a $25 flat fee, plus $20 per hour.

Explanation:

Step1: Calculate the slope (rate per hour)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(1,45)\) and \((x_2,y_2)=(2,70)\).
\(m=\frac{70 - 45}{2 - 1}=\frac{25}{1}=25\)

Step2: Find the y - intercept (flat fee)

Use the point - slope form \(y - y_1=m(x - x_1)\). Substitute \(m = 25\), \(x_1 = 1\), \(y_1=45\).
\(y-45=25(x - 1)\)
\(y-45=25x-25\)
\(y=25x + 20\)

Answer:

C. The mechanic charges a $20 flat fee, plus $25 per hour.