enter an inequality that represents the graph in the box.
Enter an inequality that represents the graph in the box.
Answer: If you’re asked to enter an inequality that represents a graph, you’ll need to interpret the graph’s key features. Here’s how you can do it:
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Identify the Slope and Y-Intercept: Look at the line on the graph to identify the slope (how steep the line is) and the y-intercept (where the line crosses the y-axis).
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Determine the Type of Line: Is the line solid or dashed? A solid line means the inequality includes the values on the line (≤ or ≥), while a dashed line means the values on the line are not included (< or >).
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Check the Shaded Area: The shaded area indicates the set of solutions. If the shading is above the line, use “>” or “≥”. If it’s below the line, use “<” or “≤”.
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Write the Inequality: Use the information gathered to write the inequality. For example, if the line has a slope of 2, a y-intercept of -3, is dashed, and the shading is below, the inequality would be:
$$y < 2x - 3$$ -
Verify Points: Select a point in the shaded area and substitute it into your inequality to verify it satisfies the condition.
Summary: To represent a graph with an inequality, determine the line’s slope and y-intercept, check if it’s solid or dashed, note where the shading is, and write the inequality accordingly. Verify with a point in the shaded region to ensure accuracy.