@eSpeX
Write the equation of the line that is perpendicular to the line y = 2x + 2 and passes through the point (6, 3).

y = 2x + 6
y = -one halfx + 3
y = -one halfx + 6
y = 2x + 3

Question

@eSpeX
Write the equation of the line that is perpendicular to the line y = 2x + 2 and passes through the point (6, 3).

 y = 2x + 6
 y = -one halfx + 3
 y = -one halfx + 6
 y = 2x + 3

anonymous · Answer

sort of the same thing

espex · Answer

This one is very much like the one we just did. Yes, the difference between a parallel line and a perpendicular line is that the slope is inverted.

espex · Answer

So first identify your slope, your $x_1$ and your $y_1$

anonymous · Answer

like absolute value

espex · Answer

Like flipping a fraction.

espex · Answer

So what is the slope of your existing line?

anonymous · Answer

it is 2

espex · Answer

Okay, that means then, that your perpendicular line has a slope of $\frac{1}{2}$

anonymous · Answer

ok so up one over 2

matlee · Answer

it does not turn negative? aw man i put that on my end of course exam today lol

anonymous · Answer

sorry bout that

espex · Answer

Yes, @matlee , I dropped a sign, thank you.

espex · Answer

Your slope is $-\frac{1}{2}$ sorry for that confusion

anonymous · Answer

oh so down 1 over 2

espex · Answer

@ro561man do you recall the equation we were working with previously?

anonymous · Answer

yeah

espex · Answer

$y-y_1=m(x-x_1)$ 
So what is the 'm', $x_1$, and $y_1$?

matlee · Answer

No sorry i did not mean to correct you i just had to guess on that one

anonymous · Answer

m=2  x1=6  y1=3

espex · Answer

@matlee it's always good to have a second or third pair of eyes when teaching. :) Thank you.

espex · Answer

@ro561man So the slope for a perpendicular line is....?

espex · Answer

And put them together in the equation.

anonymous · Answer

-2

espex · Answer

Reverse the sign and flip

anonymous · Answer

oh srry 
y-3=-2[3-x]

espex · Answer

$y-3=-\frac{1}{2}(x-6)$

anonymous · Answer

oh it has to b a fraction

espex · Answer

In some cases, yes. If you have a slope of 3, and you want a perpendicular line, the slope will be $-\frac{1}{3}$, however, if you have a slope of $\frac{1}{2}$ and you want the perpendicular, it would be -2.

espex · Answer

So no matter what it is, you reverse the sign and flip it.

espex · Answer

Anyway, you now have $y-3=-\frac{1}{2}(x-6)$, put it into slope/intercept form and you have the answer.

anonymous · Answer

thank you so much