Aline segment whose endpoints are (2,6) and (8,y) is perpendicular to a line whose slope is -4. what is the value of y?

If the line segment is perpendicular to a line with the slope of -4, that means the line segment has a slope of 1/4.

First let's make an equation for the line segment using the slope of 1/4 and the point at (2,6) to find the final piece, the y-intercept

y = mx + b
6 = 1/4(2) + b
6 = 2/4 + b
24/4 = 2/4 + b
22/4 = b

y = 1/4 x + 22/4
6 = 1/4(2) + 22/4
6 = 2/4 + 22/4
6 = 24/4
6 = 6 <-- proves that this equation is correct

Now you may plug in the x to find y. ( 8 , y )
y = 1/4(8) + 22/4
y = 8/4 + 22/4
y = 30/4 = 15/2 = 7.5