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I’m given a problem in which I need to calculate the values for a, b, c where a>0 where the equation for a straight line ax+by-c=0 and this line passes through then points (0,7) and (-2,0).

Here’s what I have got:

ax+by-c=0

by=c-ax therefore when the line crosses at (-2,0) this equation can be arranged as follows 0=c-a(-2)

I have done this for the other coordinates, therefore 0=c-b(7).

At this point I’m lost because I can’t see a possible connection between the two equations. Am I proceeding along the right path, or have I completed got it wrong?

Thanks, Pavadrin