Math CentralQuandaries & Queries


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?


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