Question

Rewrite the equation of a line in point-slope form to slope intercept form: y-2=2/3(6x+9)

Answer 1

You have this:
y-2=2/3(6x+9)
You want to transform that into this:
y=mx+b
What do you think the first step should be?

Answer 2

Simplify so +2?

Answer 3

Not quite yet. First you want to distribute 2/3 into (6x+9)
Do you remember how to do that?

Answer 4

yes so 4x+6?

Answer 5

Yep!
y-2=4x+6
Looks much better now, right? NOW we can add two to both sides. How would the equation look after we do that?

Answer 6

It would be y=4x+8

Answer 7

Correct! And since the equation is now in slope intercept form, that's your answer!

Answer 8

Thank you! but theres a few more, if you could help that would be greaaaat!

Answer 9

If I know how to do it, I'll help!

Answer 10

Alright. So you know what a y-intercept is, correct?

Answer 11

Somewhat

Answer 12

Well all you need to know for now is that the y-intercept is where the line crosses the y-axis. Looking at the graph, can you tell what the y-intercept is?

Answer 13

0,2

Answer 14

Yes. But we can just call it 2. So let's plug that into the slope intercept formula.
y = mx + 2
Next, we want to find m. What would we look at to find that?

Answer 15

The x intercept?

Answer 16

Not quite.. We would look at the slope of the line. Also known as rise/run.
What is the rise/run of this graph?

Answer 17

I honestly dont know :s

Answer 18

Okay.. The rise of a line is how much distance up/downward the line moves to get to the next point. Run is the distance left/right. Like this.

Answer 19

Do you understand?

Answer 20

yes but there arent any points

Answer 21

or is it 10,3?

Answer 22

@jim_thompson5910

Answer 23

Sure there are. Points are formed whenever a line crosses defined coordinates. The next point up would be at (1, 5).

Answer 24

....? Im losyt

Answer 25

I'm sorry. I guess I'm not explaining this clearly enough. A good way to spot where the next "point" on a line is, is to look wherever the line passes through the center of a "+" on the grid. Is that understandable, or is it still confusing?

Answer 26

Yes, I understand, what would I need to do next?

Answer 27

We still need to find the rise and the run. As you can see on the graph, the distance between (0, 2), and (1, 5) is 3 up, 1 across. Making the slope 3/1, which is 3.
So where would that go in the formula
y = mx + 2 ?

Answer 28

m=3

Answer 29

Yep! And that's the equation of the line in slope intercept form!
y = 3x + 2

Answer 30

thankyou, I need help with just 3 more

Answer 31

Write the equation of a line in slope intercept form that is parallel to the line y=1/3x+5 and passes through (-9, 5).

Answer 32

Okay. So here are both of our equations at this point.
y = (1/3)x+5
y = mx + b

Answer 33

So as we discussed earlier, if two lines are parallel, then they share the same slope. So plug the slope into the second equation.

Answer 34

y=5/(1/3)?

Answer 35

Hmm?

Answer 36

...

Answer 37

I'm not sure what you did there.
The equation that we are trying to find has to have the same slope as the equation we are given. (1/3)
Plug (1/3) into
y = mx+b

Answer 38

1/3=b?

Answer 39

or m?

Answer 40

m is always the slope. (1/3) = m
So we have
y = (1/3)x + b
We need to find b. But we are already given the x and y values (-9, 5).
Plug those into the equation we already have.
y=(1/3)x+b

Answer 41

y=(1/3)x+-4?

Answer 42

No. Don't add the two values together, just plug them into the equation..
5 = (1/3)(-9) + b
Now solve the equation for b.

Answer 43

b=5

Answer 44

@tHe_FiZiCx99

Answer 45

I'm guessing that you aren't understanding the things that I am explaining?

Answer 46

If not, it's fine. I have been doing this for quite a bit, so this may be a sign that I need to take a break.

Answer 47

But here is the rest of the problem. You multiply (1/3) and (-9) to get -3, then you add that to both sides to get b = 8.
We then get the equation y =(1/3)x + 8

Answer 48

And that's your answer.