Math CentralQuandaries & Queries


Question from Diana, a student:

find an equation in general form Ax + By = C with the following properties passing through points (a,b) and (2a, 2b)

Hi Diana,

I am going to help you how to find two facts about the line Ax + BY = C.

  1. What is the slope of the line that passes through (a, b) and (2a, 2b)?

  2. Substitute (a, b) and (2a, 2b) into the equation of the line to get

    Aa + Bb = C and
    2Aa + 2Bb = C

    Multiply the first equation by 2 and subtract the two equations. What does that tell you about C?

What is the equation of the line that satisfies 1 and 2?


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