Question

use the equation of the line of best fit, ( y = 1.85x + 11.30 ), 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 works 10 hours? (b) what is the predicted amount of money spent on entertainment for a student who doesnt work any hours? (c) for an increase of one hour in time worked, what is the predicted increase in the amount of money spent on entertainment?

Explanation:

Step1: Solve part (a)

Substitute \(x = 10\) into \(y=1.85x + 11.30\).
\(y=1.85\times10+11.30\)
\(y = 18.5+11.30\)
\(y=29.8\)

Step2: Solve part (b)

Substitute \(x = 0\) into \(y=1.85x + 11.30\).
\(y=1.85\times0+11.30\)
\(y=0 + 11.30\)
\(y = 11.30\)

Step3: Solve part (c)

The equation of the line is in the form \(y=mx + b\), where \(m\) is the slope. In \(y = 1.85x+11.30\), the slope \(m = 1.85\). For a linear function \(y=mx + b\), when \(x\) increases by \(1\) (i.e., \(\Delta x=1\)), \(\Delta y=m\Delta x\). Since \(m = 1.85\) and \(\Delta x = 1\), \(\Delta y=1.85\)

Answer:

(a) \(\$29.8\)
(b) \(\$11.30\)
(c) \(\$1.85\)