Question

WRITE AN EQUATION IN SLOPE-INTERCEPT, POINT-SLOPE, OR STANDARD FORM FOR THE LINE WITH THE GIVEN INFORMATION. EXPLAIN WHY YOU CHOSE THE FORM YOU USED.

a. passes through (-1, 4) and (-5, 2) (standard form)
b. slope 2, y-intercept -4 (slope-intercept)
c. has an x-intercept of 6 and a y-intercept of 3 (standard form)
d. passes through (1, 2) with slope -5/3 (point-slope)

Answer 1

I figured out which form they're in by common knowledge and I know how to explain WHY I choose each form, but I don't know how to write and equation in each form, and I mainly need help with that. Please and thank you :D Medals will be given to best/most helpful answer(s).

Answer 2

Point-Slope Formula \((y-y_1)=m(x-x_1)\)
Slope-Intercept Formula \(y=mx+b\)

Answer 3

so for the point-slope equation I would put (2 - -5) = m(1 - 3)? Is that correct?

And for slope-intercept equation I would put -4 = m2 + b? Is that correct?

I'm sorry if I'm being difficult I'm just not so good with these sort of things.

Answer 4

On the Point-Slope, you will choose a point and substitute the values for x and y in place of \(x_1\) and \(y_1\). Also, find the slope and plug that in for m.

Answer 5

Do I choose any slope? And how would I find the slope?

Answer 6

I meant any point. Oops :3

Answer 7

Slope is the change in \(y\) over the change in \(x\).
The formula looks like this:
\[\frac{y_2-y_1}{x_2-x_1}\]

Answer 8

And yes, you can choose any point on the line to create the equation.

Answer 9

Okay I understand how to use the formula, but what would I input into it to find the slope?

Answer 10

Line? Does this mean I have to draw a graph in order to find my point?

Answer 11

Point 1 (-1,4)
Point 2 (-5,2)
Slope: \(m=\frac{2-4}{-5-(-1)}\)
No, you do not have to draw a graph, just choose one of the given points.

Answer 12

Oh okay, that makes sense lol. Thank you, I would've never figured this stuff out on my own.

Answer 13

You are welcome. FYI: www.purplemath.com is also a good resource.

Answer 14

Thanks a lot, so once I figured out the slope with the formula, take one of the given points and insert them in the equation?

Answer 15

Exactly! :-)

Answer 16

So say if I chose point 1 (-1, 4) it would be, (4 - 4) = 3.8(-1 - [-1]) ?

Answer 17

Too many numbers. You still need the x and y in the equation. Only substitute one point for the \(x_1\) and \(y_1\).

Answer 18

So it would be (y - 4) = 3.8(x - [-1])?

Answer 19

Mostly. Where did the 3.8 come from?

Answer 20

Oops I meant 0.5, I think I accidentally copied and pasted that into the equation from a different problem.

Answer 21

In that case, you are correct. And that should change your choice of equation format.

Answer 22

How would that change the equation format?

Answer 23

You answered standards form. It has been a few years so I could be wrong, but I believe the equation you just wrote is in point-slope form.

Answer 24

I thought the format you gave me was point-slope form?

Answer 25

Yes, the formula I gave you is Point-Slope, but you answered Standard Form up at the top. I believe your answer should be Point-Slope.

Answer 26

Oh okay I get what you were saying now, it actually gave me the correct formula. Thank you.

Answer 27

Glad to help. How are you doing on the others?

Answer 28

Not so good, haha.

Answer 29

B should be easier - use the Slope-Intercept form since that is the information that you have.

Answer 30

How do I find x-intercept? and do I just leave the variable b as is?

Answer 31

Not sure why you would want the x-intercept...
\{y=mx+b\) where m=slope and b= y-intercept.

Answer 32

So I don't need the find x? and do I find the slope as the same way as before?

Answer 33

Slope = 2, y-intercept = -4
That information was given.

Answer 34

Nevermind I forgot the slope was already there

Answer 35

\(:-)\)

Answer 36

So it would be y = 2x + -4?

Answer 37

That is the answer I got.

Answer 38

Oh that's simple lol, could you help me with next one?

Answer 39

c?
I can help you get to the equation taking the scenic route. You would be better off reposting that question.

Answer 40

Yes c and okay.

Answer 41

d is similar to a with less steps.

Answer 42

c. has an x-intercept of 6 and a y-intercept of 3 (I believe it's Standard Form)

Answer 43

I don't know an easy way to get to the equation from there. I'm sure there is a formula or quick method, but I don't know it. Using the Point-Slope Formula will work, but I think there is an easier way.

Answer 44

I'm going to sign off soon - do you want to work on d?

Answer 45

Yea let's work on d

Answer 46

I think I figured d out, is it (y - 2) = -1.67(x - 1)