Question

the lines described by y=(5a+3x) and y=-1/2x are perpendicular. what is the value of a?

Answer 1

the slopes of your lines are determined by the coefficients of the x terms of your equations.
They are 3 for the first one, and -1/2 for the second.
Since their product is not equal to -1, they cannot be perpendicular no matter what the value of a is
The 5a term has nothing to do with the slopes.

Perhaps you have the brackets in the wrong place

e.g. if it had been y = (5a+3)x then it would make sense.
set (5a+3)*(-1/2) = -1 and solve for a

Answer 2

The slope product of two perpendicular lines must be -1.

In your case, the slope of the first line is 3, and of the second line is -1/2, so the lines cannot be perpendicular whatever a is.

Are you sure you did not mean to write
y = ax + 5 for the first line? The a needs to be part of the slope coefficient if you want to make the lines perpendicular.

Answer 3

Proof that great minds think alike, lol

Answer 4

I was thinking exactly the same thing as I read the two responses.