I got intercept = (3, 0); y-intercept = (0, -4). Am I right?
You have an equation for a line, remember that:
the x intercept is where y = 0 and the y intercept is where x = 0
So set each one to zero in your equation and check your answer:
3x - 4y = -12
for the y intercept x = 0
-4y = -12
y = 3
so... (0,3) is your answer
for the x intercept y = 0
3x = -12
x = -4
and... (-4,0) is your answer
it looks like you've confused your answers.
Remember that if the line intercepts the x axis it's because the value of y at that point is zero.
And if the line intercepts the y axis its because the value of x at that point equals zero.
On the y axis, there is no value for x.
On the x axis there is no value for y.
When you get to 3D:
on the x axis there is no value for y and z
on the y axis there is no value for x and z
on the z axis there is no value for x and y
This would be much easier to demonstrate with a drawing but I have to operate within the constraints of the website. Anyways, I hope I helped you out.