SOLUTION: how do you write an equation of a line thru the given pts. in Ax+By=C form? (4,1) (6,3) Helpppp Pleaase!

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Question 418286: how do you write an equation of a line thru the given pts. in Ax+By=C form?
(4,1) (6,3)
Helpppp Pleaase!
Found 2 solutions by josmiceli, Edwin McCravy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
the points are:
(x1,y1) , (x2,y2)
The formula is:
+%28y+-+y1%29+%2F+%28x+-+x1%29+=+%28y2+-+y1%29+%2F+%28x2+-+x1%29+
given:
(4,1) (6,3)
+%28y+-+1%29+%2F+%28x+-+4%29+=+%283+-+1%29+%2F+%286+-+4%29+
+%28y+-+1%29+%2F+%28x+-+4%29+=+1+
+y+-+1+=+x+-+4
y+=+x+-+3
check answer:
(6,3)
y+=+x+-+3
3+=+6+-+3
3+=+3
OK
(4,1)
y+=+x+-+3
1+=+4+-+3
1+=+1
OK

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
how do you write an equation of a line thru the given pts. in Ax+By=C form?
(4,1) (6,3)


The other tutor did it correctly but by a slightly different method and
also it needs to be placed in the form Ax + By = C, not the form he left
it in.

Use the slope formula: x%5B1%5D=4, y%5B1%5D=1, x%5B2%5D=6, y%5B2%5D=3

m+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

m+=+%283-1%29%2F%286-4%29

m+=+2%2F2

m+=+1

Use the point-slope formula:

y+-+y%5B1%5D=m%28x-x%5B1%5D%29

y - 1 = 1(x-4)

y - 1 = x - 4

y - x = -3

Swap the terms on the left to get x first because Ax+By=C has x first

-x + y = -3

Make the coefficient of x positive by multiplying every
term by -1 which changes the sign of ever term on both sides:

x - y = 3

That's the answer in Ax + By = C form 

where A=1,  B = -1, and C = 3

You could write it this way

1x + (-1)y = 3

to show both the A and the B, but probably you just want

x - y = 3

Edwin