Write an equation in slope intercept form: Perpendicular to -8x+9y=82 through (-8,-2)

Question

Just need a little help please!

Answer 1

Hey there, Ashley!

Looks like the first thing you want to do is get the first line into slope-intercept form, (y=mx+b, where m is slope and b is the y-intercept) so you can identify the slope.

-8x+9y=82

Isolate the y.

-8x +8x + 9y = 82 + 8x

9y/9 = 8/9(x) + 9 1/9

y = (8/9)x + 9 1/9

So, the first slope is (8/9), which means that the perpendicular slope (which is a negative reciprocal of the given linear slope) is (-9/8).

Let's use that.

Your new line, in slope-intercept form, starts with y and multiplies x by the slope:

y = (-9/8)x + b

Now to figure out that y-intercept. The point you've been given will help, but you'll need to rearrange the formula to solve for b and find the y-int.

Given: (-8, -2)

y - (-9/8)x = (-9/8)x - (9/8)x + b

y + (9/8)x = b

Now, use the point coordinates.

(-2) + (9/8)(-8) = b

-2 - 9 = b

b = -11

Now, you've got your slope (-9/8) and your y-int (-11). Put them back in the formula as m and b:

y = (-9/8)x - 11

There's your new line! Hope this helped.