Question

the scatter plot shows the time spent watching tv, x, and the time spent doing homework, y, by each of 25 students last week.
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?
(b) what is the predicted time spent doing homework for a student who spends 12 hours watching tv?
(c) for an increase of one hour in the time spent watching tv, what is the predicted decrease in the time spent doing homework?

Explanation:

Step1: Substitute \(x = 0\) into the equation \(y=-0.76x + 26.04\)

When \(x = 0\), \(y=-0.76\times0+26.04\)

Step2: Calculate the value of \(y\)

\(y = 26.04\)

Step3: Substitute \(x = 12\) into the equation \(y=-0.76x + 26.04\)

\(y=-0.76\times12+26.04\)

Step4: Calculate the value of \(y\)

\(y=-9.12 + 26.04=16.92\)

Step5: Analyze the slope - intercept form \(y = mx + b\)

The equation of the line is \(y=-0.76x + 26.04\), where \(m=-0.76\) and \(b = 26.04\). In the linear equation \(y=mx + b\), the slope \(m\) represents the rate of change. For an increase of \(1\) in \(x\), the change in \(y\) is \(m\).

Answer:

(a) \(26.04\) hours
(b) \(16.92\) hours
(c) \(0.76\) hours