### Home > A2C > Chapter 5 > Lesson 5.2.2 > Problem5-83

5-83.

Graph the solutions to each of the following inequalities on a different set of axes (but you should be able to fit all four on one side of the graph paper). Label each graph with the inequality as given and with its $y$-form. Choose a test point and show that it gives the same result in both forms of your inequality.

1. $3x − 3 \lt y$

$y \gt 3x − 3$

1. $3 \gt y$

$y \lt 3$

1. $3x − 2y ≤ 6$

Rewrite the inequality as an equation and solve for y. Graph the line.

Does the point (0, 0) make the original inequality true?

You need to decide whether to use ≥ or ≤. Since (0, 0) worked in the original inequality, it should work in the one you are writing as well. Try one symbol and test (0, 0). If it is not true, try it the other way.

$\textit{y} \ge \frac{3}{2} \textit{x} -2$

1. $x^{2} − y ≤ 9$

Repeat the steps used in part (a): Solve for y; graph the parabola; test (0, 0); decide where to shade.

$y ≥ x^{2} − 9$