Question

question 16 of 17 (1 point) | question attempt: 1 of unlimited
use the equation of the line of best fit, ( y=-0.76x + 26.04 ), 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? hours
(b) for an increase of one hour in the time spent watching tv, what is the predicted decrease in the time spent doing homework? hours
(c) what is the predicted time spent doing homework for a student who spends 18 hours watching tv? hours

Explanation:

Step1: Solve part (a)

Substitute \(x = 0\) into \(y=-0.76x + 26.04\).
\(y=-0.76\times0+26.04\)

Step2: Solve part (b)

The slope of the line \(y = mx + b\) (here \(m=-0.76\), \(b = 26.04\)) gives the rate of change. For a linear function \(y=mx + b\), when \(x\) increases by 1, \(y\) changes by \(m\).

Step3: Solve part (c)

Substitute \(x = 18\) into \(y=-0.76x + 26.04\).
\(y=-0.76\times18+26.04\)
First, calculate \(-0.76\times18=-13.68\). Then \(y=-13.68 + 26.04\)

Answer:

a. \(26.04\) hours
b. \(0.76\) hours
c. \(12.36\) hours