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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)
oops i put my x's on top. (y1-y2)/(x1-x2)
Ok so (-3-(-8)/(7-4)?
yes (-3-(-8))/(7-4) Do the subtraction on top and then do the subtraction on bottom.
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.
So -3*3=5(7)/3*3+b = 9=35+b?
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
Ok. So next I need to get 3b on the left side right?
Well you could leave it on the right and do something with that 35 instead but yeah either way really.
Okay so -9 - 35 = 35 - 35 +3b?
Okay so -44 = 3b?
And then -44/3 = 3b/3 which equals -14 2/3 =3b?
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
We should be able to rearrange this into the form you want Ax+By=C
Did you subtract 5x/3 on both sides? Looks like you subtracted on one side but not the other.
Yes. Now get rid of fractional part by multiplying both sides by 3 and you are done.
So -5x + y = -44?
You need to also multiply that one term by 3.
3(-5x/3+y=-44/3) 3(-5x/3+y)=3(-44/3) 3(-5x/3)+3(y)=3(-44/3) -5x + 3y = -44
Ohh! Alright! Thank you!
You did good. Good job Dani.