To determine which linear inequality corresponds to the graph, we need to analyze the options provided based on the typical characteristics of a linear inequality graph.
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y < 3x - 1: This inequality suggests that the area below the line \(y = 3x - 1\) is shaded. The line will have a slope of 3 and intersect the y-axis at -1.
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y < (1/3)x - 1: This inequality suggests that the area below the line \(y = (1/3)x - 1\) is shaded. The line will have a slope of \(1/3\) and intersect the y-axis at -1.
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y > 2x - 1: This inequality suggests that the area above the line \(y = 2x - 1\) is shaded. The line will have a slope of 2 and intersect the y-axis at -1.
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y > (1/3)x - 1: This inequality suggests that the area above the line \(y = (1/3)x - 1\) is shaded, similar to option 3 but with a smaller slope.
To choose among the options, we should look for specific characteristics in the graph you have. Here's how to identify the correct inequality:
- If the region below the line is shaded, choose y < 3x - 1 or y < (1/3)x - 1.
- If the region above the line is shaded, choose y > 2x - 1 or y > (1/3)x - 1.
- Also consider whether the line is dashed (indicating < or >) or solid (indicating ≤ or ≥).
If you can provide a description of the graph (e.g., the slope of the line, points where it intersects the axes, and which area is shaded), it will help narrow it down further. Otherwise, you can match the options based on the slope and y-intercept characteristics.