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 Question from Danielle, a student: Hello, could you help me figure out what the equation of the line is in the form of Ax+By=C with the points (-2,0) and (0,3)? Thank You!

Hi Danielle,

I am going to illustrate with two different points, $(-5, 0) \mbox{ and } (7, 3).$

There are a number of different ways of writing the equation of a line, and I usually use $y - y_1 = m(x - x_1)$ where $(x_1, y_1)$ is a point on the line and $m$ is the slope of the line. If you have two points on the line $(x_1, y_1) \mbox{ and } (x_2, y_2)$ then you can determine the slope using

$m = \frac{y_2 - y_1}{x_2 - x_1}$

For my points I am going to let $(x_1, y_1) = (-5, 0)$ and $(y_1, y_2) = (7, 3).$ Thus the slope is

$m = \frac{3 - 0}{7 - (-5)} = \frac{3}{12} = \frac14$

The equation of the line is thus

$y - y_1 = m(x - x_1) \mbox{ or } y - 0 = \frac14 (x - (-5))$

If you now multiply both sides by 4 you get $4y = x + 5$ which is almost what you need. If you subtract $4y$ from each side and subtract $5$ from each side the equation becomes $x - 4y = -5.$