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 we can put into y=mx+b form first then rearrange it to the standard form.
So m represents slope and b is the y-intercept.
Given two points, you can use the slope formula which is
(x1-x2)/(y1-y2)

Answer 2

So (7-4)/(-3-(-8)?

Answer 3

oops i put my x's on top.
(y1-y2)/(x1-x2)

Answer 4

Ok so (-3-(-8)/(7-4)?

Answer 5

yes
(-3-(-8))/(7-4)

Do the subtraction on top and then do the subtraction on bottom.

Answer 6

So 5/3

Answer 7

yes that is m, the slope
so let's fill in the info we have
y=5x/3+b

The only thing we don't know now is b, the y-intercept.

you can use a point on the line (either of the two given to you) to find b.

So if we use (7,-3) then we will see we have only one know in the following equation

-3=5(7)/3+b

Solve for b.

Answer 8

So -3*3=5(7)/3*3+b = 9=35+b?

Answer 9

Well if you are multiplying both sides by 3 to get rid of that fraction then you can't forget to multiply each term on the right hand side by 3.
So you should have
-3*3=5(7)/3*3+3*b

Answer 10

-9=35+3b

Answer 11

Ok. So next I need to get 3b on the left side right?

Answer 12

Well you could leave it on the right and do something with that 35 instead but yeah either way really.

Answer 13

Okay so -9 - 35 = 35 - 35 +3b?

Answer 14

yep yep

Answer 15

Okay so -44 = 3b?

Answer 16

yep

Answer 17

And then -44/3 = 3b/3 which equals -14 2/3 =3b?

Answer 18

Yes I would leave it just in the improper form.

So we have m=5/3 and b=-44/3

This means y=mx+b ---> y=5x/3-44/3

Answer 19

We should be able to rearrange this into the form you want Ax+By=C

Answer 20

So 5x/3+y=-44/3?

Answer 21

Did you subtract 5x/3 on both sides? Looks like you subtracted on one side but not the other.

Answer 22

So -5x/3+y=-44/3?

Answer 23

Yes.
Now get rid of fractional part by multiplying both sides by 3 and you are done.

Answer 24

So -5x + y = -44?

Answer 25

You need to also multiply that one term by 3.

Answer 26

3(-5x/3+y=-44/3)
3(-5x/3+y)=3(-44/3)
3(-5x/3)+3(y)=3(-44/3)
-5x + 3y = -44

Answer 27

Ohh! Alright! Thank you!

Answer 28

You did good. Good job Dani.