I have a graph that shows a ---- kind of 3 line above the solid line for x & y. My assignment is as follows. Whe have graphed the boundary line for the liear inequality. Determine the correct half-plane. y >3 First how do I solve and 2 how do I graph it?

Question

I have a graph that shows a ---- kind of 3 line above the solid line for x & y. My assignment is as follows. Whe have graphed the boundary line for the liear inequality. Determine the correct half-plane. y >3 First how do I solve and 2 how do I graph it?

If the allowed area is y greater than 3, then the line y=3 divides the allowed area, it is the boundry line. Everything above the line is allowed.

Answer 1

To solve and graph the linear inequality y > 3, you can follow these steps:

1. Start by graphing the equation of the boundary line, which is y = 3. This line is a horizontal line that passes through the y-axis at the point (0, 3).

2. Since the inequality is y > 3, we want to shade the region above the boundary line. You can do this by drawing a dashed line for y = 3 (indicating that it is not included in the solution) and shading the area above the line.

Here's a step-by-step guide:

Step 1: Graph the boundary line y = 3.
- Plot the point (0, 3) on the y-axis.
- Draw a dashed horizontal line passing through (0, 3).

Step 2: Shade the region above the boundary line.
- Since the inequality is y > 3, shade the area above the dashed line.
- You can do this by lightly shading the area above the line or drawing diagonal lines pointing upward.

Step 3: Label the shaded region as the solution.
- Write "y > 3" next to or inside the shaded region to indicate that any point above the line satisfies the inequality.

And that's it! You have solved and graphed the linear inequality y > 3.

Answer 2

To solve the linear inequality y > 3, you can follow these steps:

1. Start by graphing the line y = 3. This line will be a horizontal line that intersects the y-axis at the point (0, 3).

2. Since the inequality is y > 3, the boundary line should be a dashed line instead of a solid line. This indicates that the points on the line itself are not included in the solution set.

3. To determine which half-plane is the correct one, you need to consider the inequality y > 3. Since the inequality is y greater than 3, the correct half-plane is the one above the line y = 3.

4. Shade the region above the line y = 3. This shaded region represents the solutions to the inequality y > 3.

By following these steps, you will be able to solve the inequality and graph the correct half-plane.