Graph this inequality: y < 1. Plot points on the boundary line. Select the line to switch between solid and dotted. Select a region to shade it.
Understand the Problem
The question is asking how to graph the inequality y < 1, indicating the need to plot points, select the appropriate boundary line type (solid or dotted), and shade the correct region.
Answer
Graph a dotted line at $y = 1$ and shade the region below it.
Answer for screen readers
The graph will consist of a dotted horizontal line at $y=1$ with the region below the line shaded.
Steps to Solve
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Identify the Boundary Line The inequality given is $y < 1$. The boundary line is where $y = 1$.
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Plot the Boundary Line Since the inequality is "<" (not inclusive), we use a dotted line for the boundary to indicate that points on the line are not part of the solution. Draw this line horizontally at $y = 1$ across the graph.
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Determine the Shading Region Since the inequality $y < 1$ means that $y$ values are less than 1, shade the region below the line. This represents all the points where $y$ is less than 1.
The graph will consist of a dotted horizontal line at $y=1$ with the region below the line shaded.
More Information
This inequality represents all points where the y-coordinate is less than 1. The dotted line indicates that points on the line itself (where $y$ equals 1) are not included in the solution set.
Tips
- Forgetting to use a dotted line instead of a solid line, which would inaccurately include points where $y=1$.
- Shading the wrong region; make sure to shade below the line for $y < 1$.
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