To analyze the given inequality \( y \leq -\frac{5}{2}x - 2 \), we can interpret it as follows:
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Identify the slope and y-intercept: The inequality \( y \leq -\frac{5}{2}x - 2 \) represents a linear equation \( y = -\frac{5}{2}x - 2 \). Here, the slope is \(-\frac{5}{2}\) and the y-intercept is \(-2\).
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Graph the equation:
- To graph the line \( y = -\frac{5}{2}x - 2 \), you can plot the y-intercept at the point (0, -2).
- Next, use the slope to find another point. Since the slope is \(-\frac{5}{2}\), from the point (0, -2), you can move down 5 units and to the right 2 units to reach the point (2, -7).
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Draw the line: Once you have at least two points, draw the line through these points. Since the inequality is "less than or equal to" (\(\leq\)), the line should be solid, indicating that points on the line are included in the solution set.
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Shading the region: Since the inequality is \( y \leq -\frac{5}{2}x - 2\), you will shade the region below the line. This shaded area represents all the points (x, y) that satisfy the inequality.
Thus, the solution to the inequality consists of all points that are located on or below the line \( y = -\frac{5}{2}x - 2 \).