Graph the inequality y 2x - 2.

The boundary line is $y = 2x - 2$. You have already correctly drawn this line. Since the inequality is $y \ge 2x - 2$, the line should be solid (continuous), which matches your drawing.

Pick a point that is not on the line. The easiest point to use is often the origin $(0, 0)$.

Substitute $x = 0$ and $y = 0$ into the inequality $y \ge 2x - 2$:

The statement $0 \ge -2$ is true.
Since the test point $(0, 0)$ satisfies the inequality, and $(0, 0)$ is located above the line $y = 2x - 2$ (relative to the y-intercept at $(0, -2)$), you should shade the region above the line.

• If the inequality were $y \ge 2x - 2$, you would shade the region above the solid line.
• If the inequality were $y \le 2x - 2$, you would shade the region below the solid line.
• If the inequality were $y > 2x - 2$, you would draw a dashed line and shade the region above it.
• If the inequality were $y < 2x - 2$, you would draw a dashed line and shade the region below it.

For the inequality $y \ge 2x - 2$, you should shade the region above the line $y = 2x - 2$.