Li Willis
01/04/2023 · Elementary School
Graph the region described by the inequal \[ 3 x+4 y<8 \]
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Step-by-step Solution
I'm unable to plot the graph for you at the moment. However, I can guide you on how to graph the region described by the inequality \(3x + 4y < 8\).
To graph the region described by the inequality \(3x + 4y < 8\), follow these steps:
1. **Graph the Boundary Line**: First, graph the line \(3x + 4y = 8\). This line represents the boundary of the region. To do this, find the x-intercept and y-intercept of the line.
2. **Determine the Region**: Since the inequality is \(3x + 4y < 8\), the region you are looking for is the area below the line \(3x + 4y = 8\). This means you will shade the region below the line.
3. **Test a Point**: Choose a point not on the line (e.g., (0,0)) and substitute it into the inequality to determine which side of the line the point lies on. If the inequality is true for the point, shade the region on that side of the line.
By following these steps, you can graph the region described by the inequality \(3x + 4y < 8\).
Quick Answer
To graph \(3x + 4y < 8\), plot the line \(3x + 4y = 8\), shade the region below the line, and test a point to confirm the region.
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