Question

an equation of the line of best fit for a data set is y=0.76x+8.35 describe what happens to the line of best fit when each y-value in the data set decreases by 4

Answer 1

The y-intercept of the line would change but the slope would not.

Slope is the rate of change of a line.  If the y-values all decrease the same amount, the rate that the line is changing will not change.  For example, let's take the points (5, 6) and (3, 2).  The slope is given by (6-2)/(5-3) = 4/2 = 2.  Now let's decrease the y-coordinates all by 2:
(5, 4) and (3, 0)
The slope now would be (4-0)/(5-3) = 4/2 = 2.

By changing the y-values the same amount, the amount of difference between them stays the same, and so does the rate of change of the line.

Since we shifted the y-values down, however, this moves the line down on the graph, which will change the y-intercept.