Question

What is the equation of the line in slope-intercept form that passes through the point (1, 3) and is perpendicular to the line y = –x + 2?

Answer 1

do you know what the slope of \(y=-x+2\) is ?

Answer 2

-1?

Answer 3

yes

Answer 4

do you know what the slope of the perpendicular line would be?

Answer 5

no, thats what i'm having trouble understanding. Is it -1?

Answer 6

no

Answer 7

if the slope of a line is \(m\) then the perpendicular line will have slope \(-\frac{1}{m}\) sometimes called the "negative reciprocal"

Answer 8

oh ok

Answer 9

so for example if the slope of a line is 2, the perpendicular line will have slope \(-\frac{1}{2}\)

Answer 10

and if the slope of a line is \(-\frac{3}{4}\) the perpendicular line will have slope \(\frac{4}{3}\)

Answer 11

so would it be -1/1?

Answer 12

your slope is already negative, it is \(-1\)
the perpendicular line will have a positive slope

Answer 13

so 1/1

Answer 14

yeah, better known as \(1\)

Answer 15

lol, yeah. ok, i understand, so then how do we get the y-intercept? Do we keep it from the equation? So for instance it would be y=x+2

Answer 16

?*

Answer 17

now that you have the slope is 1, and the point is \((1,3)\) use the "point - slope" formula

Answer 18

\[y-y_1=m(x-x_1)\]
\[y-3=1(x-1)\]
\[y=x+2\] yeah you have it
it was silly of me to write the 1 there, just to make it clear

Answer 19

I just did that on my paper! Cool! I fully understand this now, thank you so much for helping me. You're really the best!

Answer 20

yw