math
posted by Kelsie on .
How do I put an equation into standard form, Ax+Bx=C?
I have the given points (1,3) and (2,4).
Also, how do you write an equation in standard form when perpendicular through another?
[the question is "through (1,2) and perpendicular to 2x3y=5]

first use y2y1/x2x1 to find the slope
43/2(1)=7/3
then(assuming the equation is parellel)use point slope form yy=slope(xx)
y3=7/3(x(1))
y3=7/3x7/3
y=7/3x+2/3
then to put it in standard form it must be in the Ax+By=C form with no fractions and the leading coefficient cannot be negative.
y=7/3x+2/3
7/3x+y=2/3
3(7/3x+y=2/3)
7x+y=2 
the way i would work it is first move the equation to standard form because i find it easier to work it that way.
2x3y=5
3y=2x5
y=2/3x+5/3
an equation perpendicular to this equation would have a slope of 3/2 because perpendicular lines have opposite recirocal slopes. now use point slope.
y2=3/2(x(1))
y2=3/2x3/2
y=3/2x+1/2
now move the equation back to standard form.
y=3/2x+1/2
3/2x+y=1/2
2(3/2x+y=1/2)
3x+y=1