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## beatboxingfetus one year ago 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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1. beatboxingfetus

Don't know how to do this one!

2. 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

3. rvc

equation of line parallel to given line has the same slope

4. Littlebird

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

5. beatboxingfetus

I don't understand.

6. rvc

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

7. beatboxingfetus

would it be y = 4x - 4

8. beatboxingfetus

I'm so confused.

9. rvc

the first question what is the slope ?

10. 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)

11. 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

12. rvc

yeah

13. beatboxingfetus

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

14. beatboxingfetus

8 or 3?

15. 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)

16. rvc

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

17. beatboxingfetus

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

18. rvc

os is lagging :(

19. beatboxingfetus

It really always lags a lot.

20. rvc

All the best!

21. 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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