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Consider the line 4x-8y= -6.

What is the slope of a line perpendicular to this line?

What is the slope of a line parallel to this line​

User Fazier
by
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1 Answer

6 votes

Answer:

  • Perpendicular slope = -2
  • Parallel slope = 1/2

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Step-by-step explanation:

Let's solve for y to get the equation into y = mx+b form, aka slope intercept form.

4x-8y= -6

-8y= -6-4x

y = (-6-4x)/(-8)

y = -6/(-8) + (-4x)/(-8)

y = 3/4 + (1/2)x

y = (1/2)x + 3/4

This is now in y = mx+b form

m = 1/2 = slope

b = 3/4 = y intercept

We'll ignore the y intercept and focus on the slope only.

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Rule: If the slope of a line is a/b, then the perpendicular slope is -b/a

Flip the fraction and flip the sign.

In this case, the original slope 1/2 has a perpendicular slope of -2/1 or simply -2.

The original slope multiplied with the perpendicular slope yields -1. So (1/2)*(-2/1) = -1

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Another rule: Two parallel lines always have equal slopes, but different y intercepts.

The original slope is 1/2, so the parallel slope is also 1/2.

User Bryanzpope
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