Question

use the equation of the line of best fit, ( y = 1.83x + 11.34 ), to answer the questions below.
give exact answers, not rounded approximations.
(a) what is the predicted amount of money spent on entertainment for a student who doesnt work any hours?
( $square )
(b) what is the predicted amount of money spent on entertainment for a student who works 12 hours?
( $square )
(c) for an increase of one hour in time worked, what is the predicted increase in the amount of money spent on entertainment?
( $square )

Explanation:

Step1: Find the value when \(x = 0\)

The equation of the line is \(y=1.83x + 11.34\). When \(x = 0\) (student doesn't work any hours), substitute \(x = 0\) into the equation:
\(y=1.83\times0+11.34\)
\(y = 11.34\)

Step2: Find the value when \(x = 12\)

Substitute \(x = 12\) into the equation \(y=1.83x + 11.34\):
\(y=1.83\times12+11.34\)
First, calculate \(1.83\times12=21.96\)
Then, \(y=21.96 + 11.34=33.3\)

Step3: Find the slope - related value

The slope of the line \(y = mx + b\) is \(m\). In the equation \(y=1.83x + 11.34\), the slope \(m=- 1.83\). The slope represents the change in \(y\) (amount of money spent on entertainment) per unit change in \(x\) (number of hours worked). So for an increase of one hour in time worked, the predicted decrease in the amount of money spent on entertainment is \(1.83\) dollars.

Answer:

(a) \(\$11.34\)
(b) \(\$33.3\)
(c) \(\$1.83\)