The standard form Ax+By=C

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Question from Susan, a student:

I am having difficulty changing the point-slope form of the equation of the line y-y1=m(x-x1) to the standard form Ax+By=C. You must express A,B,C in terms of the constants m,x1,y1. I have been able to insert numbers and switch easily from the general to the point slope equation, but I am stumped on how to convert it this way.

Hi Susan,

Did you try to mimic the steps you used when you had numbers?

Here is what I would do.

y - y₁ = m(x - x₁)

Expand the right side

y - y₁ = mx - mx₁

Add - mx to each side

y - y₁ - mx = mx - mx₁ - mx = -mx₁

Add y₁ to each side

y - y₁ - mx + y₁ = -mx + y₁

y - mx = y₁ - mx₁

Does this help?

Penny

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