Question

The graph of the equation $x + 2y + 3 = 0$ is perpendicular to the graph of the equation $ax + 2y + 3 = 0$. What is the value of $a$?

Answer 1

a = -4.

Explanation:

If the are perpendicular then the slope of one graph will be - 1 / slope of the other.

Convert each equation to slope-intercept form:

x + 2y + 3 = 0

2y = = -x - 3

y = (-1/2)x - 3/2 (Slope/intercept form)

So the slope of the line perpendicular to this will be - 1 / (-1/2) = 2.

Consider the other line:

ax + 2y + 3 = 0

2y = -ax - 3

y = (-a/2) x - 3/2 (Slope/intercept form)

So the slope for this line - a/2 and it equals 2.

-a/2 = 2

-a = 2*2 = 4

a = -4 (answer).