Which line represents the perpendicular of the Line x + 8y = 16

Question

Perpendicular

Answer 1

Hi Ayden,

Perpendicular lines have negative reciprocal slopes, so you need to find the slope of your line and then get a slope perpendicular to it. To get your line's slope:

x + 8y = 16

Change to slope-intercept form: y = mx + b, m = slope, b = y-intercept

8y = 16 - x

y = 2 - 1/8x

y = -1/8x + 2

m = -1/8

Slope of a perpendicular line will be the negative reciprocal of -1/8, which is 8.

So, one perpendicular line would be:

y = 8x or 8x - y = 0

But you could add any constant that interests you--i.e. y = 8x +3, 8x + 8, etc. All have negative reciprocal slopes to the initial equation. I hope this helps.

Answer 2

Hi Ayden,

We first need to get the equation into slope-intercept form (y=mx+b) so we can determine what the slope (m) is. Perpendicular lines have slopes that are negative reciprocals so once we determine the slope we can change the sign to its opposite and determine the reciprocal.

Let's first get the equation x + 8y = 16 into the form y = mx+b

First we need to move x to the right side by subtracting 1x from both sides.

8y = -x + 16

Next we need to divide both sides by 8 to get y by itself.

y = -x/8 + 2

-x/8 can be written as -1/8x. The opposite reciprocal of -1/8 is +8/1 or just 8.

The perpendicular line would be y = 8x + 2