Question

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

Answer 1

Graph the line of `(3x+4y=12)` using two arbitrary solutions;
then shade in the side of the line containing the point `(0,0)`

Explanation:

`3x+4y<=12`
includes all points on the line `3x+4y=12`

The x and y intercepts provide a convenient pair of points on this line (although any other pairs would work).
`color(white)("XXX")x=0 rarr y=4`
`color(white)("XXX")y=0 rarr x=3`
so the pairs `(0,4)` and `(3,0)` are on this line.
Plot these point and draw a line through them.

Since the inequality is true for `(x,y)=(0,0)`
the point `(0,0)` must be on the selected side of the line just drawn.
graph{3x+4y <= 12 [-10, 10, -5, 5]}