Question

Find an equation of a line through (-2,4) and perpendicular to -x+8y=16

Answer 1

What is the slope of the line -x+8y=16?

Answer 2

okay, at first we want to rearrange your equation into a y-intercept form.

\(\large\color{black}{-x+8y=16 }\)

\(\large\color{black}{-x+8y\color{red}{+x}=16\color{red}{+x} }\)

\(\large\color{black}{8y=16+x }\)

then, what do you get after dividing each term (in the equation) by 8?

Answer 3

y=2=1/8x

Answer 4

yes, you meant, y=2+1/8x , but didn't press shift hard enough the second time:)

Answer 5

So, now we need to find the perpendicular slope. can you do this, or need a hint?

Answer 6

is it -8

Answer 7

yes, correct.

Answer 8

So now we have,
\(\large\color{blue}{ \rm y=-8x+b }\)
but we need to find the "b".

Answer 9

you know that (-2,4) is one of the points on your (new) line. (That is a given).

Answer 10

can you solve for b?

Answer 11

is it -12

Answer 12

yes.

Answer 13

So your equation is now?

Answer 14

y=-8x-12

Answer 15

\(\normalsize\color{blue}{ \rm y=-8x+b }\) ....
then you found that b=-12.

Answer 16

yes.