To represent the inequality \( y < 2x - 5 \) on a graph, follow these steps:
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Graph the boundary line: First, we need to graph the line \( y = 2x - 5 \). This is a linear equation with a slope of 2 and a y-intercept of -5.
- To plot the line, start at the y-intercept (0, -5) on the y-axis.
- Use the slope (rise over run) to find another point. From (0, -5), go up 2 units (rise) and to the right 1 unit (run) to reach the point (1, -3).
- Draw a dashed line because the inequality is strict (\(<\)), meaning points on the line are not included in the solution.
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Shade the appropriate region: Since the inequality is \( y < 2x - 5 \), you'll shade the region below the line. This indicates that for any point in this region, the y-value is less than the value given by \( 2x - 5 \).
In summary, the graph of \( y < 2x - 5 \) consists of:
- A dashed line for \( y = 2x - 5 \)
- Shading below this line.
If you have multiple graph options to choose from, look for the one with a dashed line that has shading below that line.
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