Question

How do you graph `3y+4x=12`?

Answer 1

This is a straight line through `(0, 4)` and `(3, 0)`

Explanation:

Notice that the terms are linear or constant, so this equation represents a straight line.

We can find the intersections with the `x` and `y` axes by setting `y` or `x` equal to zero, or equivalently covering up the corresponding term and solving the resultant equation.

So putting `x=0` we get:

`3y = 12`

Dividing both sides by `3`, we find:

`y=4`

So the line intercepts the `y` axis (which has equation `x=0`) at the point `(0, 4)`

If we instead put `y=0` then we get:

`4x=12`

and hence:

`x=3`

So the `x` intercept is at `(3, 0)`

We can now draw our line through these two intercepts:
graph{(4x+3y-12)((x-3)^2+y^2-0.01)(x^2+(y-4)^2-0.01) = 0 [-9.21, 10.79, -2.28, 7.72]}