Question 418286
how do you write an equation of a line thru the given pts. in Ax+By=C form?
(4,1) (6,3)
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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[1]=4}}}, {{{y[1]=1}}}, {{{x[2]=6}}}, {{{y[2]=3}}}

{{{m = (y[2]-y[1])/(x[2]-x[1])}}}

{{{m = (3-1)/(6-4)}}}

{{{m = 2/2}}}

{{{m = 1}}}

Use the point-slope formula:

{{{y - y[1]=m(x-x[1])}}}

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</pre>