Which is the graph of the linear inequality $$ y

Question

Which is the graph of the linear inequality $$ y<3 x+1 $$ ?

UpStudy AI · Accepted Answer

It seems that I am unable to create the graph directly. However, I can guide you on how to graph it manually or using graphing software.

### Steps to Graph $$ y < 3x + 1 $$:

1. **Draw the boundary line**:
   - Start by plotting the line $$ y = 3x + 1 $$.
   - To find points on the line, you can use:
     - When $$ x = 0 $$: $$ y = 3(0) + 1 = 1 $$ → Point (0, 1)
     - When $$ x = 1 $$: $$ y = 3(1) + 1 = 4 $$ → Point (1, 4)
   - Plot these points and draw a dashed line through them to represent $$ y = 3x + 1 $$.

2. **Choose a test point**:
   - Use the point (0, 0) to test the inequality.

3. **Test the inequality**:
   - Substitute (0, 0) into the inequality $$ y < 3x + 1 $$:
     $$
     0 < 3(0) + 1 \implies 0 < 1
     $$
   - Since this is true, shade the region that includes the point (0, 0), which is below the dashed line.

4. **Final graph**:
   - The area below the dashed line represents all the points where $$ y < 3x + 1 $$.

You can use graphing software or a graphing calculator to visualize this more easily. Just input the equation $$ y = 3x + 1 $$ and shade the area below it.
The graph of the inequality $$ y < 3x + 1 $$ is the region below the dashed line $$ y = 3x + 1 $$.

Which is the graph of the linear inequality \( y<3 x+1 \) ?

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