Question

How do you graph the line `4x+3y-12=0`?

Answer 1

`y` intercept of the function is present at the point: `(0,4)`
and `x` intercept of the function is present at the point: `(3,0)`
See full explanation for more detail:

Explanation:

In order to clearly recognise the `x` and `y` intercepts of the function we may convert the given function to linear gradient form. That being:
`y=mx+c`
Where:

`c` is the constant determining the `y` intercept.
and `m` is the gradient of the function.

Therefore, let us do this:
`->3y=-4x+12`
Dividing both sides by `3`, we get:
`y=-4/3x+4`

This implies that the `y` intercept of the function is 4.
We can prove this via the statement:
`y` intercepts where `x=0`:
Therefore:
`y=0*x+4`
This implies that the `y` intercept of the function is present at the point: `(0,4)`

We can thus determine the `x` intercept using the statement:
`x` intercepts where `y=0`:
`->0=-4/3x+3`
`:.4/3x=4`
`x=3`
This implies that the `x` intercept of the function is present at the point: `(3,0)`

If we plot these points on a Cartesian plane and draw a line between the two, the graph has been drawn.

Attached below is a graph of the function with the intercepts in frame:

graph{y=-4/3x+4 [-9.54, 10.46, -2.92, 7.08]}