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