The inequality you provided is:

$y > 2x + 1$

To graph this inequality:

Step 1: Graph the boundary line

First, graph the equation of the line:

$y = 2x + 1$

This is a linear equation in slope-intercept form, $y = mx + b$, where $m = 2$ is the slope, and $b = 1$ is the y-intercept.

1. Plot the y-intercept: The y-intercept is the point $(0, 1)$, so mark this point on the graph.
2. Use the slope: From the y-intercept, use the slope $m = 2$, which means "rise 2 units, run 1 unit." Starting at $(0, 1)$, move 2 units up and 1 unit to the right to get another point $(1, 3)$. Repeat this for additional points if needed.
3. Draw a dashed line: Since the inequality is a strict inequality ($>$), the boundary line should be dashed to indicate that the points on the line itself are not included in the solution.

Step 2: Determine the shading

The inequality $y > 2x + 1$ means that we are looking for the region above the line. To confirm this:

• Pick a test point not on the line, such as $(0, 0)$, and substitute into the inequality.

$0 > 2(0) + 1 \quad \Rightarrow \quad 0 > 1$

This is false, so the point $(0, 0)$ is not in the solution region. Thus, the correct region to shade is the region above the line.

Would you like more details on how to graph this or any questions about these steps?

Related Questions:

1. How do you graph inequalities with horizontal or vertical lines?
2. What changes in the graph if the inequality is $y \geq 2x + 1$?
3. How would you solve a system of inequalities graphically?
4. What are the steps to convert inequalities to slope-intercept form if not already given?
5. How do you determine if a point lies in the solution region?

Tip: When graphing inequalities, always use a test point to verify which side of the boundary line should be shaded.