Write the equation of the line that is parallel to the line 4x - 3y = -12 and passes through the point (-3, 4).

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- beatboxingfetus

Don't know how to do this one!

- beatboxingfetus

Write the equation of the line that is parallel to the line y = -3x + 12 and passes through the point (-1, 6).
Need help with this one too

- rvc

equation of line parallel to given line has the same slope

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## More answers

- Littlebird

I would just start by changing the format to y=mx+b

- beatboxingfetus

I don't understand.

- rvc

\[\Large \bf y_{}-y_{1}=m(x_{}-x_{1}) ~~\\~~m: Slope\]
\[\Large \bf (x_{1},y_{1})=(-3,4)\]

- beatboxingfetus

would it be y = 4x - 4

- beatboxingfetus

I'm so confused.

- rvc

the first question
what is the slope ?

- Littlebird

rvc's format works too
but y= 4x-4 is wrong
First you subtract 4x from both sides and then divide everything by -3 for (y=mx+b)

- Littlebird

The logic behind these types of problems is that whatever you do on one side of the equal sign you do on the other

- rvc

yeah

- beatboxingfetus

oh whoops I forgot to divide everything.
y= 4/3x + 8?

- beatboxingfetus

8 or 3?

- Littlebird

4x - 3y = -12
subtract 4x from both sides
-3y = -4x - 12
divide everything by -3 on both sides
y = (4/3)x + (-12/-3)
so...
y= (4/3)x + 4
That is the original formula.
To get the parallel line you rewrite it as
y=(4/3)x + b
Plug in the provided coordinate (-3,4)

- rvc

\[4x-3y=12-->3y=4x-12-->y=\frac{4}{3}x-\frac{12}{3}\]

- beatboxingfetus

Okay I got it for both, thank you both! I wish I could give two medals.

- rvc

os is lagging :(

- beatboxingfetus

It really always lags a lot.

- rvc

All the best!

- whpalmer4

One way to do these problems is to recognize that the slope is determined by the coefficients of \(x\) and \(y\), and a parallel line has the same slope. Therefore, all you need to do is plug in your point in the original left hand side and find the new constant term:
\[4x-3y=-12\]passing through point \((-3,4)\):
\[4(-3)-3(4) = -12-12 = -24\]so the new equation is simply
\[4x-3y=-24\]
and if you solve that for \(y\) to put it in \(y = mx+b\) form (slope-intercept), you get
\[-3y=-24-4x\]\[y = \frac{4}{3}x+8\]

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