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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 2x-3y=-5]

  • math -

    first use y2-y1/x2-x1 to find the slope
    -4-3/2-(-1)=-7/3
    then(assuming the equation is parellel)use point slope form y-y=slope(x-x)
    y-3=-7/3(x-(-1))
    y-3=-7/3x-7/3
    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

  • math -

    the way i would work it is first move the equation to standard form because i find it easier to work it that way.
    2x-3y=-5
    -3y=-2x-5
    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.
    y-2=-3/2(x-(-1))
    y-2=-3/2x-3/2
    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

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