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
[tex]m\text{ = }\frac{\Delta y}{\Delta x}[/tex]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
[tex]\text{ - 0.77 = }\frac{\Delta y}{\Delta x}[/tex]We are told that x increases by 1 unit. This represents a change in x of 1 positive unit. So,
[tex]\Delta x\text{ = 1}[/tex]By replacing the value in the previous equation we have
[tex]\text{ - 0.77 = }\frac{\Delta y}{1}[/tex]So the change in the variable y is that it will decrease -0.77 whenever x increases 1 hour.
