Question

Write the equation of the line that is parallel to the line 4x - 3y = -12 and passes through the point (-3, 4).

y = four thirdsx + 8

y = four thirdsx + 3

y = -three fourthsx + 8

y = -three fourthsx + 3

Answer 1

I don't understand where you got the "+8" part in your first line of the solution up there. Can you explain that to me? I can help you.

Answer 2

I don't know the whole problem is giving me trouble

Answer 3

Ok, first of all do you know the rule about the slopes of lines that are parallel to one another?

Answer 4

I think so

Answer 5

Ok, what is the rule?

Answer 6

Sorry i don't no.

Answer 7

That's ok! The slopes of parallel lines are the same. The rule for perpendicular lines is that their slopes are negative reciprocals. So if the slope for a line is 3, a parallel line will also have the slope of 3. If a line has a slope of 3, a line that is perpendicular to it will have a slope of -1/3.

Answer 8

So your question asks for the equation of a line that is parallel to the given line. What does that tell you about the slopes of the lines? are they the same or different from each other?

Answer 9

Different

Answer 10

Read what I wrote a minute ago again. The slopes of parallel lines are the same. Keep that in mind. That is probably the part that is throwing you off. Let's go on now.

Answer 11

In order to find the slope of the first line, you have to put it into y=mx+b form. The given equation is not in that form. You have to solve it so y is alone on one side of the equation and the other stuff is on the other side. Can you solve that given equation for y and tell me what you get?

Answer 12

I don't really get it but i tried and got 19

Answer 13

That's ok. We will go step by step with the given equation. Just follow this and stop me if you get lost somewhere along the way.

Answer 14

4x - 3y = -12 is the given equation.
-3y = -12 - 4x when you isolate the y term
Ok so far?

Answer 15

yes

Answer 16

Cool. Let's move forward now then!
-3y = -12 - 4x is what we have now
Because all the terms are negative, and we absolutely HATE negative numbers, we are going to multiply the whole entire mess by -1 to make all the terms positive. Watch:

Answer 17

-1 (-3y = - 12 - 4x):
-1 times -3y is +3y; -1 times -12 is +12; -1 times -4x is +4x. Right? Cuz negative times a negative is a positive.

Answer 18

So we now have: 3y = 12 + 4x, or to make it closer to the y = mx + b format:
3y = 4x + 12. See that now?

Answer 19

yes

Answer 20

Ok, so the next thing to do is to solve for y. In other words, lose the 3 in front of it. To "undo" multiplication, we divide, so 3y/3 is just y; 4x/3 is 4/3 x; and 12/3 is 4. So the new equation when we solve for y is: y = 4/3 x + 4. Is there any part of that you don't follow?

Answer 21

no iam understanding it all thank you

Answer 22

Great! Next thing is for you to decide what the slope of that line is. Do you know it?

Answer 23

no

Answer 24

Ok the y is just the y; the number in front of the x (which is the "m" in y = mx + b) is the slope, and the "b" is the y- intercept. So if the number in front of the x is the slope, what is that number in the equation we just solved for y?

Answer 25

y = 4/3 x + 12 is the equation

Answer 26

are you saying that is the answer

Answer 27

No, I'm saying that is the slope of the equation we just solved for y, which was the given equation. The "m" is the slope. What is the slope?

Answer 28

Look at it like this, maybe it will help some:

y = m x + b
y = 4/3 x + 12

Answer 29

so to get m i divide 4 and 3

Answer 30

The m is the slope of the equation. In this case, the slope is 4/3 or to type it in words, four thirds. Four thirds is the slope of the given line.

Answer 31

You can divide it out and get 1.3333333333333 forever, but you don't need to do that. You can just leave it in fraction form. It doesn't make it harder to leave it in fraction form. It won't matter at all.

Answer 32

Would the answer be y=4/3x+3

Answer 33

You're close, but remember that the equation is found from the point-slope formula which is

\[y -y _{1}=m(x-x _{1})\]

Answer 34

The y doesn't change from a y, it's the \[y _{1}\] that changes according to what your points are. Here, your y point is 4, right? And you x point is -3. So use those and the slope you just found and fill them into the equation. What do you get?

Answer 35

\[y-y _{1}=m(x-x _{1})\]

Answer 36

\[y-4=\frac{ 4 }{ 3 }(x-(-3))\]

Answer 37

\[y-4=\frac{ 4 }{ 3 }(x+3)\]

Answer 38

Now you have to distribute the 4/3 through the parantheses. You get:\[y-4=\frac{ 4 }{ 3 }x+4\]

Answer 39

To get the y alone, you add 4 to both sides:\[y=\frac{ 4 }{ 3 }x+8\]

Answer 40

you get y=4/3x+8

Answer 41

YES! see how smart you are and didn't even know it!

Answer 42

That equation is the answer. It has the same slope of 4/3 and goes through your given points. Do you understand all that?

Answer 43

Thank you so much for your help.

Answer 44

You are so welcome! I love to help with math!

Answer 45

Anytime!

Answer 46

Thank you