Question

time spent watching tv (in hours)
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?
(b) what is the predicted time spent doing homework for a student who doesn’t spend any time watching tv?
(c) what is the predicted time spent doing homework for a student who spends 18 hours watching tv?

Explanation:

Step1: Analyze slope for part (a)

The equation of the line is $y = - 0.76x+26.04$. The slope of the line is -0.76. In a linear - relationship $y = mx + b$, the slope $m$ represents the change in $y$ for a unit change in $x$. Here, $x$ is the time spent watching TV and $y$ is the time spent doing homework. So for an increase of 1 hour in $x$ (time watching TV), the change in $y$ (time doing homework) is - 0.76 hours.

Step2: Find $y$ - intercept for part (b)

When $x = 0$ (student doesn't spend any time watching TV), we substitute $x = 0$ into the equation $y=-0.76x + 26.04$. Then $y=-0.76\times0 + 26.04=26.04$.

Step3: Substitute $x$ value for part (c)

When $x = 18$ (student spends 18 hours watching TV), we substitute $x = 18$ into the equation $y=-0.76x + 26.04$. So $y=-0.76\times18 + 26.04=-13.68+26.04 = 12.36$.

Answer:

(a) 0.76
(b) 26.04
(c) 12.36