Question

If the graph of the equation ax + 3y = 9 is perpendicular to the graph of the equation 3x + y = -4, find the value of a.

Answer 1

When you multiply the slopes of two linear equations, and you get a -1, then the lines are perpendicular.

So rearrange your first equation, so that it is in this form: y=mx+b

m is the slope of the equation.

So you you would have this: -a/3x +3 = y

So -a/3 is the slope in this equation.

Rearrange the second equation to the same form.

So it looks like this: -3x-4= y In this equation, the slope is -3.

So now you set the product of the two slopes equal to -1

So it looks like this: (-3)(-a/3)= -1

Now solve for a.

-a/3=1/3

a=1