Question

How do you graph `3x-4y \ge 12`?

Answer 1

You can manipulate the expression until it looks like something very easy to figure out:

• First of all, add `4y` on both sides, and get `3x \geq 12+4y`
• Secondly, subtract 12 from both sides, and get `3x-12 \geq 4y`
• Lastly, divide both sides by 4, and get `\frac{3}{4}x -3 \geq y`

You obviously can read this last inequality as
`y \leq \frac{3}{4}x -3`. We know that if the equality holds, `y= \frac{3}{4}x -3` represents a line, thus the inequality represents all the area below (since we have that `y` must be lesser or equal than the expression of the line) that said line. graph{y <= 3/4x -3 [-18.13, 21.87, -12.16, 7.84]} This is the graph, where you can see the line `y= \frac{3}{4}x -3` in a darker blue, while the lighter-blue painted area is the one where `y < \frac{3}{4}x -3` holds.