Question

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

Answer 1

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

Answer 2

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

Answer 3

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?

Answer 4

3y = 5x?

Answer 5

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

Answer 6

How do I simplify it?

Answer 7

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

Answer 8

Is it 2 + 3y = 6 - x ?

Answer 9

What is \(x - x\) ?

Answer 10

0? or just x?

Answer 11

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\[3y = -x + 6\]

Answer 12

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?

Answer 13

y = -x + 3 ?

Answer 14

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?

Answer 15

y = -x + 2

Answer 16

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.

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

The two a are different sorry about that.

Answer 21

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

Answer 22

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

Answer 23

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.

Answer 24

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

Answer 25

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?

Answer 26

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

Answer 27

* \(+ b\) sorry for the typo

Answer 28

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

Answer 29

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

Answer 30

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

Answer 31

I get -1 for that.

Answer 32

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?

Answer 33

Do I add +1 to b as well?

Answer 34

No. It looks like this:\[4+1 = -1 + b + 1\]Now simplfy

Answer 35

Is it 5 = b ?

Answer 36

Yayyyy! Good work.

Answer 37

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?

Answer 38

y = -1/3x +5?

Answer 39

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

Answer 40

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

Answer 41

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

Answer 42

That is true indeed. Also again thank you !

Answer 43

You're welcome