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.

Another way to find the intercepts is to begin by putting the equation into slope intercept form. (y = mx + b)

3x - 4y = -12

-3x          -3x

-4y = -3x - 12

/-4     /-4  /-4

y = (3/4)x + 3

Now, you know that your slope is 3/4 and the y-intercept is 3, or (0,3). plot the point (0,3). plug 0 into the original equation for y to find the x intercept.

3x - 4y = -12

3x - 4(0) = -12

3x - 0 = -12

3x = -12

/3    /3

x = -4

x intercept is -4, or (-4,0)

Hope this helps!