General Linear Equations?

Question

My AP calc class is reviewing and I don't remember how to write a general linear equation. I know the equation is ax+by=c. The question is to write a general linear equation for the line that passes through (0,0) and (2,3). Help, please?

Answer 1

Start by writting the equation for the line that passes through (0,0) and (2,3) in any form you can and then convert it to standard form.  You know right away since the line includes the point (0,0) that the y-intercept is 0 so all you need to write this in slope-intercept form y = mx + b is the slope.  If the line includes the points (x1,y1) and (x2,y2) then the slope is given by:

m = (y1 - y2) / (x1 - x2)

m = (0 - 3) / (0 - 2)

m = -3 / -2

m = 3/2

So the equation for the line in slope-intercept form is

y = mx + b

y = (3/2)x + 0

y = (3/2)x

Now put this in standard form.

y = (3/2)x   ...multiply both sides by 2

2y = 3x   ...subtract 2y from both sides

0 = 3x - 2y

3x - 2y = 0

This is in standard form.

Hope this helps you!