Question

use the equation of the line of best fit, $y = 0.94x + 8.06$, to answer the questions below.
give exact answers, not rounded approximations.
(a) what is the predicted hourly pay rate for a cashier who
(doesnt have any experience?
(b) for an increase of one year of experience, what is the
predicted increase in the hourly pay rate?
(c) what is the predicted hourly pay rate for a cashier with
5 years of experience?

Explanation:

Step1: Find the predicted hourly pay rate for no experience

The equation of the line of best fit is \( y = 0.94x+8.06 \). When \( x = 0 \) (no experience), substitute \( x = 0 \) into the equation:
\( y=0.94\times0 + 8.06\)
\( y = 8.06\)

Step2: Find the increase in hourly pay rate per year of experience

The slope - intercept form of a line is \( y=mx + b\), where \( m\) is the slope and \( b\) is the \( y\) - intercept. In the equation \( y = 0.94x+8.06\), the slope \( m = 0.94\). The slope represents the rate of change. So, for an increase of one year of experience (\(\Delta x=1\)), the change in \( y\) (hourly pay rate) is given by:
\(\Delta y=m\Delta x\). Since \( m = 0.94\) and \(\Delta x = 1\), \(\Delta y=0.94\)

Step3: Find the predicted hourly pay rate for 5 years of experience

Substitute \( x = 5\) into the equation \( y = 0.94x+8.06\)
\( y=0.94\times5+8.06\)
First, calculate \( 0.94\times5=4.7\)
Then, \( y=4.7 + 8.06\)
\( y=12.76\)

Answer:

a. \( 8.06 \)
b. \( 0.94 \)
c. \( 12.76 \)