Question

Write the equation of the line that is perpendicular to the line y = 2x + 2 and passes through the point (6, 3)

Answer 1

what would you say is the slope of -> y = 2x + 2 ?

Answer 2

2

Answer 3

ok, perpendicular lines have a NEGATIVE RECIPROCAL slopes
what does that mean?
well, if this has a slope of 2
any perpendicular one to it will have

reciprocal of 2
1/2

negativize that
-1/2

Answer 4

so, now you have the slope of the other line, and a point it passes through
so use both in the point-slope form
$$
\large { y-y_1=m(x-x_1)}$$

Answer 5

okay. I dont understand how to do that.

Answer 6

alright, so, we know the slope is -1/2, we know that a point it passes through is (6, 3)
so, using \(y-y_1=m(x-x_1)\)
we'll have
$$
(\color{red}{6}, \color{red}{3}), m = \color{blue}{-\frac{1}{2}}\\
y-(\color{red}{3})=\color{blue}{-\frac{1}{2}}(x-(\color{red}{6}))
$$

Answer 7

now just solve for "y", and you'd get the line equation