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Type the equation of the given line in standard form.
The line with m = 4 and intersecting 2x -4y = 8 at x = 6.
Thanks!

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- anonymous

Step #1: convert "2x -4y = 8" to y=mx+b
Step #2...

- anonymous

So that would make it -4y=2x+8?

- anonymous

Or do I have to put the m in there to and make it -4y=8x+8?

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## More answers

- anonymous

you want y not -4y so you should simplify

- anonymous

Move the 2x over to the other side (with subtraction), divide both sides by -4.
Can you write this second step @cutie.patootie ? :-)
You'll end up getting a y=mx+b form line that allows to to draw this:
|dw:1343071328047:dw|

- anonymous

-4y=2x+8 turns into..
-4y-2x=8 divide by -4 gives you..
y+(1/2)x=2
Right?

- anonymous

No... unless you wrote it incorrect at the start.
-4y + 2x = 8?
Move the x's over
-4y = -2x + 8
Divide by -4
y = 0.5 x - 2 (see graph above)

- anonymous

Oh well I had it right, but then I moved the x to the wrong side. But I see where I made my mistake now.

- anonymous

then it tells you there is some other line with:
y = 4x + b , because it says "m = 4"
An "intersection of two lines" means when they are equal to each other. If you've solved both for the dependent varible (y) that means you can set the y's equal to each other:
\(y_1 = y_2\)
we know:
\(y_1 = \frac{1}{2}x - 2\)
\(y_2 = 4x + b_2\)
So...
\(y_1 = y_2\)
\(\frac{1}{2}x - 2 = 4x + b_2\)
Make sense?
The final steps are substitute in "x=6", solve for \(b_2\), and rewrite \(y_2\)

- anonymous

Okay, so you get...
(1/2)(6) - 2 = 4(6) +b2
3-2=24+b2
1=24+b2
b2= -23?

- anonymous

You're correct!
|dw:1343072679957:dw|

- anonymous

When x = 6, they are both equal.

- anonymous

Now don't forget to rewrite \(y_2=4x-23\) in standard form :-)
All good?

- anonymous

Visual methods FTW!

- anonymous

Okay, I think I follow. So I write it y + 4x = -23?

- anonymous

And yes! Hahaha.

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