Question

Write the equation of the line that is parallel to the line 3x - y = -3 and passes through the point (4, -2).

Answer 1

First, find the slope of your line \[3x-y=-3\]You could do this by solving for \(y\), which will give you the equation in slope-intercept form: \[y = mx+b\]The slope of the line will be \(m\). Then, as parallel lines have equal slopes, plug that value of \(m\) and the known point \((x_1,y_1) = (4,-2)\) into the point-slope formula:
\[y-y_1 = m(x-x_1)\]and rearrange into whatever form you see fit.

Answer 2

Would I replace the X and Y values given, (4, -2)?
Like:
\[3(4) - ^{-}2 = ^{-}3?\]
@whpalmer4

Answer 3

I can't make any sense of what you just wrote...

First step: solve \[3x-y=-3\] for \(y\) on the left side, all alone. What do you get?

Answer 4

You're still going to have numbers and a letter on the right side

Answer 5

3x - y = -3
+ y = + y
3x = y - 3
+3 = + 3
3x + 3 = y
y = 3x + 3
I simplified the equation for you now plot that on a graph... now let's find the second equation.

Answer 6

\[3x = -3 + y?\]

Answer 7

That was in response to @whpalmer4

Answer 8

y - (-2) = 3(x - 4)
y + 2 = 3x - 12
-2 = -2
y = 3x - 10

Answer 9

Okay. so now my two equations are \[y = 3x + 3\] and \[y = 3x - 10\]

Answer 10

Wait

Answer 11

Let me check them first.

Answer 12

y - (-2) = 3(x - 4)
y + 2 = 3x - 12
-2 = -2
y = 3x - 14

Answer 13

y = 3x + 3
and
y = 3x - 14

Answer 14

Right now I'm practically clueless right now. Here's the answers:
\[y = -\frac{ 1 }{ 3 }x - 6\]\[y = -\frac{ 1 }{ 3 }x - 14\]\[y = 3x - 6\] \[y = 3x - 14\]

Answer 15

Yup, I was right y = 3x - 14.

Answer 16

This is proof of it being correct if you need proof.

Answer 17

Okay, thank you!

Answer 18

Your Welcome. :D

Answer 19

What do I open that with?

Answer 20

Yes, \[y=3x-14\] is correct. I'll go through the steps I suggested:

\[3x-y=-3\]solve for \(y\):\[3x-3x-y=-3-3x\]\[-y=-3-3x\]multiply by -1\[y = 3+3x\]compare with slope-intercept form \(y = mx+b\) and it is clear that \(m = 3\)

Now plug known point + known slope into formula:
\[y -(-2) = 3(x-4)\]Rearrange to have \(y\) alone on left:\[y = 3(x-4)+(-2)\]\[y = 3x-12-2 = 3x-14\]

Answer 21

Thank you both so much