Question

what is the equation of the line perpendicular to the line y=2/3x+2 that passes through the point (1, 5)?

Answer 1

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

Answer 2

what is the slope of that given line?

Answer 3

\[\frac{ 2 }{ 3 }\]

Answer 4

flip the fraction: 2/3 ----> 3/2

flip the sign: 3/2 ----> -3/2

Answer 5

the perpendicular slope is -3/2

Answer 6

the perpendicular line goes through (1,5)

(x,y) = (1,5)

x = 1
y = 5

Answer 7

so we have this info

m = -3/2
x = 1
y = 5

you plug those values into y = mx+b and solve for b

Answer 8

tell me what you get

Answer 9

b = 6?

Answer 10

i dont think this is right

Answer 11

but Im out of my head tonight so Im not sure

Answer 12

so y-5=-3/2 (x-1)

Answer 13

right?

Answer 14

now solve for y

Answer 15

y=1/2(13-3x)

Answer 16

that's another way of expressing

\[\Large y = -\frac{3}{2}x + \frac{13}{2}\]

Answer 17

what I wrote is in slope intercept form

m = -3/2 is the slope

b = 13/2 is the y-intercept

Answer 18

ohh okay thank you for the help!

Answer 19

you're welcome