Find the value for a for which 3y - ax = 8 and 4x + 8y = 2 are perpendicular.

Step-by-step explanation:

3y+8y=11y and -ax+4x=4ax

a = 6

Step-by-step explanation:

Perpendicular lines have slope that are negative reciprocal of each other. There product = -1

Solve both equations for y.

3y - ax = 8                                 4x + 8y = 2

3y = ax + 8                                  8y = -4x + 2

y = ax/3 + 8/3                               y = -4x/8 + 2/8

 y = a/3(x) + 8/3                              y = -1/2(x) + 1/4

Now you know that the slope of  y = -1/2(x)+ 1/4  is -1/2

and the slope of y = a/3(x) + 8/3 is a/3.  

Looking for the value of "a" that will make the lines perpendicular.

You know that one line slope is -1/2 so the other line slope is 2 because the slope are negative reciprocal.   Also remember that the slope is the coefficient of the x term.

Now   a/3 = 2 ; a = 6