Question

The scatter plot shows the time spent watching TV, X, and the time spent doing homework, y, by each of 24 students last week.For an increase of one hour in the time spent watching TV, what is the predicted decrease in the time spent doing homework? ?

Answer 1

Letting x begin the time spent watching tv and y the time spent doing homework, we are given the following linear approximation of this two variables:

y = -0.77x+26.08.

This is a linear function of the form y = mx+b where m is the slope of the line and b is the y-intercept.

Recall that one form of defining the slope is as follows

`m\text{ = }(\Delta y)/(\Delta x)`

where the "triangle " is the delta letter. In this context, delta y represents the change in the variable y, and delta x represents the change in the variable x. In our particular case, we have that m=-0.77. So we have the equation

`\text{ - 0.77 = }(\Delta y)/(\Delta x)`

We are told that x increases by 1 unit. This represents a change in x of 1 positive unit. So,

`\Delta x\text{ = 1}`

By replacing the value in the previous equation we have

`\text{ - 0.77 = }(\Delta y)/(1)`

So the change in the variable y is that it will decrease -0.77 whenever x increases 1 hour.