Questions: Determine the inequality shown in the graph below. The inequality symbols can be entered using the toolbar.

Determine the inequality shown in the graph below. The inequality symbols can be entered using the toolbar.
Transcript text: Determine the inequality shown in the graph below. The inequality symbols can be entered using the toolbar.
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Solution

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Solution Steps

Step 1: Find the equation of the line.

The line passes through the points (0, 4) and (8, 0). The slope is $m = \frac{0 - 4}{8 - 0} = \frac{-4}{8} = -\frac{1}{2}$. Since the y-intercept is 4, the equation of the line is $y = -\frac{1}{2}x + 4$.

Step 2: Determine the inequality sign.

The shaded area is below the line, so the inequality is either $y \le -\frac{1}{2}x + 4$ or $y < -\frac{1}{2}x + 4$. Since the line is solid, the inequality should include the line, which means the inequality sign is $\le$.

Final Answer

$y \le -\frac{1}{2}x + 4$

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