Can someone help me with general form for the equation of a line in algebra?

Question

The sample problem the we were given is: find an equation of the line through the points (-5, 4) and (2, -5) in the general form Ax+By+C=0. Could anyone explain how to do this? I have twenty homework problems just like this!

Answer 1

There are a couple of ways to find this.  I'll use the point-slope form of the line and go from there.

First, find the slope of the line.  The slope is the difference of the y's divided by the difference of the x's:

Difference of the y's: (4-(-5)) or (4+5) or 9

Difference of the x's: (-5 -2) or -7

Slope: -9/7

The point-slope equation has the form (y-y1)=m*(x-x1) (where m is the slope).  Plug in one of the known points for y1 and x1 (I'll use (-5,4))

(y-4)=(-9/7)*(x-(-5))

(y-4)=(-9/7)*(x+5)

Let's multiply by 7 to get rid of the fraction

7*(y-4)=-9*(x+5)

Distribute on both sides:

7y-28=-9x-45

Add 9x to both sides

9x+7y-28=-45

Add 45 to both sides:

9x+7y+17=0

Done.

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