Question

use the equation of the line of best fit, y = 1.83x + 12.34, to answer the questions below. give exact answers, not rounded approximations. (a) for an increase of one hour in time worked, what is the predicted increase in the amount of money spent on entertainment? (b) what is the predicted amount of money spent on entertainment for a student who doesnt work any hours? (c) what is the predicted amount of money spent on entertainment for a student who works 8 hours?

Explanation:

Step1: Find the increase for part (a)

The equation is \(y = 1.83x+12.34\). The slope \(m = 1.83\). For a linear equation \(y=mx + b\), the slope \(m\) represents the rate of change. So when \(x\) (time worked) increases by \(1\) (one hour), \(y\) (money spent on entertainment) increases by \(m\).

Step2: Find the value for part (b)

If \(x = 0\) (doesn't work any hours), substitute \(x = 0\) into \(y=1.83x + 12.34\). Then \(y=1.83\times0+12.34=12.34\)

Step3: Find the value for part (c)

If \(x = 8\) (works 8 hours), substitute \(x = 8\) into \(y=1.83x+12.34\). Then \(y=1.83\times8 + 12.34=14.64+12.34 = 26.98\)

Answer:

(a) \(\$1.83\)
(b) \(\$12.34\)
(c) \(\$26.98\)