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) for an increase of one hour in the time spent watching tv, what is the predicted decrease in the time spent doing homework? (square) hours (b) what is the predicted time spent doing homework for a student who doesnt spend any time watching tv? (square) hours (c) what is the predicted time spent doing homework for a student who spends 18 hours watching tv? (square) hours

Explanation:

Part (a)

Step1: Recall slope interpretation

The equation of the line of best fit is \( y = -0.76x + 26.04 \), where \( y \) is time doing homework and \( x \) is time watching TV. The slope \( m \) of a linear equation \( y = mx + b \) represents the rate of change of \( y \) with respect to \( x \).

Step2: Determine the change

Here, the slope \( m=-0.76 \). This means that for each 1 - unit increase in \( x \) (time watching TV), \( y \) (time doing homework) changes by \( -0.76 \). So the predicted decrease in time doing homework for a 1 - hour increase in time watching TV is \( 0.76 \) hours.

Step1: Identify the value of \( x \)

If a student doesn't spend any time watching TV, then \( x = 0 \).

Step2: Substitute \( x = 0 \) into the equation

We use the equation \( y=-0.76x + 26.04 \). Substitute \( x = 0 \): \( y=-0.76(0)+26.04 \).

Step3: Simplify the expression

\( -0.76\times0 = 0 \), so \( y = 26.04 \).

Step1: Identify the value of \( x \)

The student spends 18 hours watching TV, so \( x = 18 \).

Step2: Substitute \( x = 18 \) into the equation

Use the equation \( y=-0.76x + 26.04 \). Substitute \( x = 18 \): \( y=-0.76\times18+26.04 \).

Step3: Calculate the product

First, calculate \( -0.76\times18=-13.68 \).

Step4: Calculate the sum

Then, \( y=-13.68 + 26.04=12.36 \).

Answer:

\( 0.76 \)

Part (b)