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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)
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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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Parallel lines have the same slope. Can you determine the slope of the given line?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I do not know how to find the slope of these two.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0OK. 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?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No. You are given\[x+3y=6\]Now subtract \(x\) from both sides\[x+3yx = 6x\]What's left after simplifying?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0How do I simplify it?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Combine like terms on the left hand side. The right hand side can't be simplified any further.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is it 2 + 3y = 6  x ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.01  1 = 0 5  5 = 0 x  x = 0 So, after simplifying you are left with\[3y = 6x\]It will be easier to understand if we write it as\[3y = x + 6\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now 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?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The 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?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0OK. 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.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Like this:\[3y = x + 6\]\[\frac{ 3y }{ 3 } = \frac{ x }{ 3 } + \frac{ 6 }{ 3 } = \frac{ 1 }{ 3 }x + 2\]See what I mean?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I was confused of that turning into a decimal I see now.

Plasmataco
 one year ago
Best ResponseYou've already chosen the best response.0Ok. So you got the slope y+a=1/3(x+a)

Plasmataco
 one year ago
Best ResponseYou've already chosen the best response.0The two a are different sorry about that.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is it supposed to be written as y = 1/3x +2 ? Or no y into it?

Plasmataco
 one year ago
Best ResponseYou've already chosen the best response.0Now, 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0OK. 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 ycoordinates of the given point.

Plasmataco
 one year ago
Best ResponseYou've already chosen the best response.0Well, there are 2 ways to write it. I find my way uses less calculations

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You 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?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is the 1 I get from 1/3(3) supposed to be b?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0* \(+ b\) sorry for the typo

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I made a typo. It should read\[4 = \frac{ 1 }{ 3 }\left( 3 \right) + b\]sorry bout that

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Its no problem ! I do not get how to solve for b.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0OK. What do you get when you multiply 1/3 x 3 ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Great. 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?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Do I add +1 to b as well?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No. It looks like this:\[4+1 = 1 + b + 1\]Now simplfy

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now 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?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Perfect. Well done. That is the line that is parallel to \(x+3y=6\) that passes through \((3, 4)\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you so much for your help! Also thank you for your time and patience! Math is my worst subject.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You're doing a good job. With some additional practice maybe math could be your best subject :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That is true indeed. Also again thank you !
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