Solved: "Find the slope that is perpendicular to the..."

High School
Algebra
Algebra I
Forms of linear equations

Danika Mckay

Answered question

2022-10-22

Find the slope that is perpendicular to the line y=−1

Answer & Explanation

Bridget Acevedo

Beginner2022-10-23Added 19 answers

The slope m of a line passing through points

(x_{1}, y_{1})

and

(x_{2}, y_{2})

is given by the formula:

m = \frac{Δ y}{Δ x} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}

The line y=−1 passes through the points (0,−1) and (1,−1). So it has slope:

\frac{(- 1) - (- 1)}{1 - 0} = \frac{0}{1} = 0

Alternatively, simply note that y=−1 can be rewritten:
y=0x+(−1)
which is in standard slope intercept form:
y=mx+b
with slope m=0 and intercept b=−1.
If a line has non-zero slope m, then any line perpendicular to it will have slope

- \frac{1}{m}

.
The line y=−1 has slope 0 so any line perpendicular to it will have undefined slope. If you try to evaluate

- \frac{1}{m}

, it involves division by 0, which has undefined result.

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