The equation of line AB is (y-3)= 5 (x-4). What is the slope of a line perpendicular to line AB?

1 Answer
Jun 5, 2018

-1/5

Explanation:

By definition, two perpendicular lines, say barX and barY, have slopes such that m_Y=1/-m_X.

To simplify, just take the negative reciprocal of one line to get the slope of a perpendicular line.

In your case, the slope of bar(AB) is 5, as detailed by the given point-slope equation. If you're confused as to why this is, refer to the bottom of this answer.

If we plug 5 into the equation above, we can see:

m_(AB')=1/-m_(AB)
m_(AB')=1/-(5)
m_(AB')=-1/5

Assume bar(AB') is the line perpendicular to bar(AB).

Here I'll explain how I got 5 as the slope of the line from this equation:

The general form of point-slope form is:

(y-y_1)=m(x-x_1)

Where
y_1 is the y-value of a point on the line,
x_1 is the x-value of the same point, and
m is the slope of the line.

Hence, I was able to figure out that in your case, the slope of your initial line was 5. (I figured this might be helpful for people who didn't recognize point-slope form.)

Hope this helps!