Question

use the equation of the line of best fit, $y=-0.77x + 26.08$, to answer the questions below. give exact answers, not rounded approximations. (a) what is the predicted time spent doing homework for a student who doesnt spend any time watching tv? (b) for an increase of one hour in the time spent watching tv, what is the predicted decrease in the time spent doing homework? (c) what is the predicted time spent doing homework for a student who spends 15 hours watching tv?

Explanation:

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

The equation of the line of best - fit is \(y=-0.77x + 26.08\). When \(x = 0\) (student doesn't spend any time watching TV), we substitute \(x = 0\) into the equation:
\(y=-0.77\times0+26.08\)
\(y = 26.08\)

Step2: Interpret the slope (for part b)

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 \(y=-0.77x + 26.08\), the slope \(m=-0.77\). The slope \(m=\frac{\Delta y}{\Delta x}\). For a change in \(x\) (time spent watching TV) of \(\Delta x = 1\) hour, the change in \(y\) (time spent doing homework) is \(\Delta y=m\times\Delta x\). Since \(m=-0.77\) and \(\Delta x = 1\), the predicted decrease in \(y\) (time spent doing homework) is \(0.77\) hours.

Step3: Substitute \(x = 15\) (for part c)

Substitute \(x = 15\) into the equation \(y=-0.77x + 26.08\).

$$
LATEXBLOCK0
$$

Answer:

(a) \(26.08\) hours
(b) \(0.77\) hours
(c) \(14.53\) hours