Question

3. What is the slope of a line perpendicular to the line with equation y = 4x + 5?
(Points : 4)
4
–4

–5

Answer 1

\[
y=4x+5 \implies -4x+1y = 5\implies \mathbf n = \langle -4,1\rangle
\]

Answer 2

A perpendicular line's normal vector would be \(\langle 1,4\rangle\).

Answer 3

So we have: \[
x + 4y=b\implies 4y=-x+b \implies y=-\frac x4+\frac b4
\]So the slope we are getting is \(-1/4\).

Answer 4

In general, we have: \[
y=mx+b \implies \mathbf n = \langle -m,1 \rangle
\]And the perpendicular normal vector will be \( \langle 1,m\rangle \).
This means: \[
x+my =c \implies y = -\frac{x}{n}+\frac cm
\]So the slope of the perpendicular line is always \(-1/m\), i.e. the negative inverse.