What is the equation of the line passing through (-3,2) with
y-intercept two thirds of the x-intercept.
Let's draw an arbitrary line through (-3,2) that crosses the
y-axis at (0,b), where "b" is the y-intercept, and the x-axis
at (a,0) where "a" is the x-intercept.
Using the distance formula on (0,b) and (a,0) we find that
the slope is
Since we are told that the y-intercept "b" is two-thirds of the
x-intercept "a", we can write
So the slope is 
We use the point slope formula to find the equation
of the line through the point (-3,2) with slope :
So the line goes through the origin and has this graph:
So we see that the x-intercept and the y-intercept are both zero,
and they coincide at the origin (0,0). And, surprisingly, that's
correct, since two-thirds of zero is indeed zero! :)
Answer:
Edwin
