Question

Given two points on the line, input the equation of the line in standard form Ax + By = C. Reduce all fractional answers to lowest terms. (7, -3), (4, -8)

Answer 1

well first you want to solve the equation of a line by using the y-intercept form
y = mx + b
obtain or solve for your slope (m)
then plug one of the coordinates into the point-slope form
y-y1 = m(x-x1)

once that is done, you can then rearrange your equation into the standard form Ax+By = c
A has to be positive and everything has to be in whole numbers

Answer 2

Thank you ^.^ but my issue is that I can't figure out how to get everything into whole numbers ;-;

Answer 3

what are the values you have?

Answer 4

or better yet, what is your y-intercept form?

Answer 5

The only things I was given is the coordinates (7, -3), (4, -8)

Answer 6

solve the equation using the y-intercept form first. follow the steps I provided

Answer 7

without rearanging I got y=1 2/3x+17 1/3

Answer 8

assuming that your y-intercept is correct
rearrange it so that it is in the form of Ax+By = c
then we'll worry about turning them into whole numbers after

Answer 9

I think it's 1 2/3x +y=17 1/3

Answer 10

so what you wanted to do is move the x value into the left side, correct?
for you to accomplish that, you need to subtract that same value on both sides of the equation. it will cancel out the x on the right side and leave you an x value on the left

Answer 11

So that would be either 5/3x=17 1/3-y, or 5/3x=(-y)+17 1/3?

Answer 12

?

Answer 13

get a pen and paper, write things down

Answer 14

I am writing things down. I'm sorry, I'm really bad at this. I got 5/3x=17 1/3-y

Answer 15

you want the x and y on the left side
you said you had y=1 2/3x+17 1/3

so if you want to move the x value into the left side so it sits besides the y, you want to subtract whatever you have as x on both sides - the left and right of the equation

-5/3x + y = -5/3x + 5/3x + 52/3

Answer 16

does it make sense?

Answer 17

OH. Oopsies. So would that be the final answer, or do I need to do more to it?
And I think it makes sense

Answer 18

if you read what I put earlier, the x value has to be POSITIVE and EVERYTHING has to be WHOLE NUMBERS

Answer 19

I thought fractions werent whole numbers though .-.

Answer 20

right now our x is negative and everything is pretty much in improper fraction form

but notice how all of our denominator is 3? and since our x is negative we want to multiply it with another negative to make it positive (negative times negative equals positive)

Answer 21

4/4 is a fraction it is a whole number since 4/4 = 1

Answer 22

I'm sorry, I meant fractions like 5/3, and 52/3

Answer 23

what about them? those are improper fractions, I converted them to that form (I hope you know how to do and undo that), so that when we make everything a whole number, you will see a nifty trick

Answer 24

so what do you think we should multiply everything by so that they all are whole numbers and so that our x becomes positive?

Answer 25

Yeah, I know hot to undo it. And..would -3/3 work?

Answer 26

if I had 9/2 and I want to convert it to whole number, all I need to do is multiply it by 2

9/2 * 2 = 9

if I had 97/5 and want to make it a whole number, all I need to do is multiply it by 5

97/5 * 5 = 97

if I had -67/15 and would like to make it a positive whole number, all I need to do is multiply it by -15

-97/5 * -15 = 97

see the pattern here?

Answer 27

So multiply by -3? I got 5x-3y=52. Am I doing this right?

Answer 28

there you go, you've converted something into standard form of equation of a line

Answer 29

Thank you! So much c:

Answer 30

And your help will be too ^.^

Answer 31

Good night, and thanks again ^.^