## anonymous one year ago Find the equation of the line and write in general form. Line parallel to the line x + 3y = 6 through (3, 4)

1. anonymous

Parallel lines have the same slope. Can you determine the slope of the given line?

2. anonymous

I do not know how to find the slope of these two.

3. anonymous

OK. You need to rearrange the given equation of the line into the form $$y=mx+b$$So first thing is to get rid of the $$x$$ on the left hand side by subtracting $$x$$ from both sides. What do you get?

4. anonymous

3y = 5x?

5. anonymous

No. You are given$x+3y=6$Now subtract $$x$$ from both sides$x+3y-x = 6-x$What's left after simplifying?

6. anonymous

How do I simplify it?

7. anonymous

Combine like terms on the left hand side. The right hand side can't be simplified any further.

8. anonymous

Is it 2 + 3y = 6 - x ?

9. anonymous

What is $$x - x$$ ?

10. anonymous

0? or just x?

11. anonymous

1 - 1 = 0 5 - 5 = 0 x - x = 0 So, after simplifying you are left with$3y = 6-x$It will be easier to understand if we write it as$3y = -x + 6$

12. anonymous

Now to get it into the form $$y=mx+b$$ you need to get rid of the 3 on the left hand side by dividing both sides by 3. What do you get?

13. anonymous

y = -x + 3 ?

14. anonymous

The left hand side is OK. But you didn't divide the -x by 3 and 6/3 is not 3. Can you fix it up?

15. anonymous

y = -x + 2

16. anonymous

OK. But you still haven't divided the -x by 3. When you divide both sides of an equation by 3, you must divide EVERY term by 3.

17. anonymous

Like this:$3y = -x + 6$$\frac{ 3y }{ 3 } = \frac{ -x }{ 3 } + \frac{ 6 }{ 3 } = -\frac{ 1 }{ 3 }x + 2$See what I mean?

18. anonymous

I was confused of that turning into a decimal I see now.

19. Plasmataco

Ok. So you got the slope y+a=-1/3(x+a)

20. Plasmataco

The two a are different sorry about that.

21. anonymous

Is it supposed to be written as y = -1/3x +2 ? Or no y into it?

22. Plasmataco

Now, you plug in the y in the coordinates given int the a next to y. If it is positive, subtract it from y, if the y in the coordinates are negative, add it to the y

23. anonymous

OK. So the slope of the given line is $$-\frac{1}{3}$$. So the line you're after has that same slope. The general form of the equation of a line is $y=mx+b$and m represents the slope, so the line you're after looks like$y=-\frac{ 1 }{ 3 }x + b$Now to solve for b, us the x- and y-coordinates of the given point.

24. Plasmataco

Well, there are 2 ways to write it. I find my way uses less calculations

25. anonymous

You are given$\left( x, y \right) = \left( 3,4 \right)$By substitution, then,$y = -\frac{ 1 }{ 3 }x + b$$4 = -\frac{ 1 }{ 3 }\left( 3 \right) = b$Can you solve this for b?

26. anonymous

Is the -1 I get from -1/3(3) supposed to be b?

27. anonymous

* $$+ b$$ sorry for the typo

28. anonymous

I made a typo. It should read$4 = -\frac{ 1 }{ 3 }\left( 3 \right) + b$sorry bout that

29. anonymous

Its no problem ! I do not get how to solve for b.

30. anonymous

OK. What do you get when you multiply -1/3 x 3 ?

31. anonymous

I get -1 for that.

32. anonymous

Great. So now you have$4 = -1 + b$To solve for b, you need to get rid of the -1 on the right hand side. To do this add 1 to both sides. What do you get?

33. anonymous

Do I add +1 to b as well?

34. anonymous

No. It looks like this:$4+1 = -1 + b + 1$Now simplfy

35. anonymous

Is it 5 = b ?

36. anonymous

Yayyyy! Good work.

37. anonymous

Now you have everything you need for the answer. The general form of the equation of a line is $y=mx + b$You calculated the slope (m) earlier and you just figured out b. Put it all together. What's the equation of the line?

38. anonymous

y = -1/3x +5?

39. anonymous

Perfect. Well done. That is the line that is parallel to $$x+3y=6$$ that passes through $$(3, 4)$$

40. anonymous

Thank you so much for your help! Also thank you for your time and patience! Math is my worst subject.

41. anonymous

You're doing a good job. With some additional practice maybe math could be your best subject :)

42. anonymous

That is true indeed. Also again thank you !

43. anonymous

You're welcome

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