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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)

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  1. anonymous
    • one year ago
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    Parallel lines have the same slope. Can you determine the slope of the given line?

  2. anonymous
    • one year ago
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    I do not know how to find the slope of these two.

  3. anonymous
    • one year ago
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    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
    • one year ago
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    3y = 5x?

  5. anonymous
    • one year ago
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    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
    • one year ago
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    How do I simplify it?

  7. anonymous
    • one year ago
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    Combine like terms on the left hand side. The right hand side can't be simplified any further.

  8. anonymous
    • one year ago
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    Is it 2 + 3y = 6 - x ?

  9. anonymous
    • one year ago
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    What is \(x - x\) ?

  10. anonymous
    • one year ago
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    0? or just x?

  11. anonymous
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    y = -x + 3 ?

  14. anonymous
    • one year ago
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    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
    • one year ago
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    y = -x + 2

  16. anonymous
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    I was confused of that turning into a decimal I see now.

  19. Plasmataco
    • one year ago
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    Ok. So you got the slope y+a=-1/3(x+a)

  20. Plasmataco
    • one year ago
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    The two a are different sorry about that.

  21. anonymous
    • one year ago
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    Is it supposed to be written as y = -1/3x +2 ? Or no y into it?

  22. Plasmataco
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    Well, there are 2 ways to write it. I find my way uses less calculations

  25. anonymous
    • one year ago
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    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
    • one year ago
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    Is the -1 I get from -1/3(3) supposed to be b?

  27. anonymous
    • one year ago
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    * \(+ b\) sorry for the typo

  28. anonymous
    • one year ago
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    I made a typo. It should read\[4 = -\frac{ 1 }{ 3 }\left( 3 \right) + b\]sorry bout that

  29. anonymous
    • one year ago
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    Its no problem ! I do not get how to solve for b.

  30. anonymous
    • one year ago
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    OK. What do you get when you multiply -1/3 x 3 ?

  31. anonymous
    • one year ago
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    I get -1 for that.

  32. anonymous
    • one year ago
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    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
    • one year ago
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    Do I add +1 to b as well?

  34. anonymous
    • one year ago
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    No. It looks like this:\[4+1 = -1 + b + 1\]Now simplfy

  35. anonymous
    • one year ago
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    Is it 5 = b ?

  36. anonymous
    • one year ago
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    Yayyyy! Good work.

  37. anonymous
    • one year ago
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    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
    • one year ago
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    y = -1/3x +5?

  39. anonymous
    • one year ago
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    Perfect. Well done. That is the line that is parallel to \(x+3y=6\) that passes through \((3, 4)\)

  40. anonymous
    • one year ago
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    Thank you so much for your help! Also thank you for your time and patience! Math is my worst subject.

  41. anonymous
    • one year ago
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    You're doing a good job. With some additional practice maybe math could be your best subject :)

  42. anonymous
    • one year ago
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    That is true indeed. Also again thank you !

  43. anonymous
    • one year ago
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    You're welcome

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