Find the slope of a line that is perpendicular to the line y=x/−5−7

Jimena Hatfield

Jimena Hatfield

Answered question

2022-09-12

Find the slope of a line that is perpendicular to the line y = x - 5 - 7

Answer & Explanation

Yasmin Lam

Yasmin Lam

Beginner2022-09-13Added 13 answers

y = x - 5 - 7 = - 1 5 x - 7
is the equation of a line with slope - 1 5 and intercept −7
If a line has slope m, then any line perpendicular to it will have slope - 1 m .
So a line perpendicular to your line of slope - 1 5 will have slope 5.
One way I like to picture this is as follows:
Suppose a line is given in slope-intercept form as
y=mx+c
where m is the slope and c the intercept.
If we reflect that line in the line y=x then the effect will be to swap the x and y coordinates, giving a line with equation:
x=my+c
If we reflect this new line in the x-axis then the result is to reverse the sign of the y coordinate, resulting in a line with equation:
x=−my+c
The total geometric effect of these two reflections is a rotation around the origin by a right angle, that is our new line is perpendicular to the old line.
Next let's rearrange into slope, intercept format. First subtract c from both sides to get:
−my=x−c
Then divide both sides by −m to get:
y = - 1 m x + c m

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?