Question

What is the slope of a line perpendicular to the line whose equation is 3x + y = -4.

Fully reduce your answer.

Answer 1

1/3

Explanation:

When the equation of a line is in standard form:

ax +by = c

We can find its slope by solving for y:

by = -ax +c

y = -a/bx +c/b

The slope is the coefficient of x. The slope is -a/b.

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A perpendicular line has a slope that is the negative reciprocal of this:

slope of perpendicular line = -1/(-a/b) = b/a

In the given equation, a=3, b=1, so the slope of the perpendicular line is ...

b/a = 1/3