Question

1 1. **Write the equation of the line that is perpendicular to and goes through the point (-8,2) 2 Week 14 Homework Packet.pdf 220.128 VIEW US

Answer 1

the given line is

$y=-\frac{1}{2}x+4$

it has slope m equal to

$m=-\frac{1}{2}$

anb y-intercept b equal to 4.

Since we need a perpendicular line, we know that this new line must have a "reciprocal inverse" slope mp for the

given m, that is

$m_p=-\frac{1}{m}$

In our case,

$m_p=-\frac{1}{-\frac{1}{2}}$

which is equal to,

$m_p=2$

Hence, the form of our perpendicular line is

$\begin{gathered} y=m_px+c \\ or \\ y=2x+c \end{gathered}$

we only need the y-intercept c. In order to find c, we must use the given point (-8,2).

By substituying this point into the last equation, we have

$2=2(-8)+c$

hence,

$\begin{gathered} 2=-16+c \\ c=2+16 \\ c=18 \end{gathered}$

Finally, the perpendicular line is

$y=2x+18$