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

Jan 21, 2015

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

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

You obviously can read this last inequality as
$y \setminus \le q \setminus \frac{3}{4} x - 3$. We know that if the equality holds, $y = \setminus \frac{3}{4} x - 3$ 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 $y = \setminus \frac{3}{4} x - 3$ in a darker blue, while the lighter-blue painted area is the one where $y < \setminus \frac{3}{4} x - 3$ holds.