Question

Which equation represents the line passing through the point (4, −16) and is perpendicular to the line y equals negative two thirds x plus 8? y equals two thirds x minus 22 y equals negative two thirds x minus 22 y equals negative three halves x minus 22 y equals three halves x minus 22

Answer 1

\[y=-\frac{2}{3}x+8\]??

Answer 2

yes

Answer 3

ok first question is do you know what the slope of \(y=-\frac{2}{3}x+8\) is ?

Answer 4

-2/3

Answer 5

ok good
next question is do you know what the slope of a perpendicular line will be?

Answer 6

if not, say "idk" and i will tell you

Answer 7

no idea, sorry

Answer 8

ok fine

Answer 9

it is the "negative reciprocal" in other words flip it and change the sign

Answer 10

so since the line has slope \(-\frac{2}{3}\) the perpendicular line will have slope \(\frac{3}{2}\)

Answer 11

so 3/2?

Answer 12

yes

Answer 13

that should eliminate some answers right away, but we can go ahead and find the equation for the line using the point - slope formula
do you know that one?

Answer 14

no

Answer 15

ok it is
\[y-y_1=m(x-x_1)\]

Answer 16

wait, y=mx+b?

Answer 17

oh nvm

Answer 18

no, that is the "slope intercept" form

Answer 19

put
\[y-y_1=m(x-x_1)\] make a direct substitution with
\[x_1=4,y_1=-16,m=\frac{3}{2}\]

Answer 20

you get
\[y-(16)=\frac{3}{2}(x-4)\] or
\[y+16=\frac{3}{2}(x-4)\]

Answer 21

then multiply out on the left to get
\[y+16=\frac{3}{2}x-6\] so
\[y=\frac{3}{2}x-22\]

Answer 22

i hope that is one of the choices!

Answer 23

it is thank you so much!