give me a problem similiar to graph >more than or equal to 2x-3

Answer 1

Sure! Here’s a similar problem for you:

Problem: Graph the inequality \( y < -\frac{1}{2}x + 4 \).

To solve this problem, follow these steps:

1. Rewrite the inequality in slope-intercept form (if necessary).
2. Graph the boundary line \( y = -\frac{1}{2}x + 4 \) as a dashed line since the inequality is "less than" (not inclusive).
3. Shade the region below the line to indicate the area where the inequality holds true.

Would you like help with the solution steps or a different problem?

Answer 2

give me a lesson on how to answer it

Answer 3

Absolutely! Here's a step-by-step lesson on how to solve and graph the inequality \( y < -\frac{1}{2}x + 4 \).

Step 1: Understand the Components of the Inequality

The inequality \( y < -\frac{1}{2}x + 4 \) has the following components:

• Slope: The coefficient of \( x \) is \(-\frac{1}{2}\), which means for every 1 unit increase in \( x \), \( y \) decreases by \( \frac{1}{2} \).
• Y-intercept: The constant term is \( 4 \), which means the line intersects the y-axis at the point \( (0, 4) \).

Step 2: Graph the Boundary Line

1. Find the y-intercept:

   • Plot the point \( (0, 4) \) on the graph.

2. Use the slope to find a second point:

   • Since the slope is \( -\frac{1}{2} \), from \( (0, 4) \), move down 1 unit and right 2 units to find another point. This gives you the point \( (2, 3) \).

3. Draw the line:

   • Connect the two points \( (0, 4) \) and \( (2, 3) \).
   • Since the inequality is \( < \) (not \(\leq\)), draw a dashed line to indicate that the points on the line are not included in the solution set.

Step 3: Determine Which Side to Shade

1. Choose a test point:
   • A common test point is the origin \( (0, 0) \). Substitute \( x = 0 \) and \( y = 0 \) into the inequality: \[ 0 < -\frac{1}{2}(0) + 4 \] Simplifying gives: \[ 0 < 4 , (\text{true}) \]
   • Since this statement is true, we shade the area that includes the point \( (0, 0) \), which is below the line.

Step 4: Finalize the Graph

• Make sure to clearly indicate the dashed line and the shaded region. The shaded area represents all the points \( (x,y) \) that satisfy the inequality \( y < -\frac{1}{2}x + 4 \).

Summary

1. Identify the slope and y-intercept.
2. Graph the boundary line using a dashed line for \( < \).
3. Use a test point to determine which side of the line to shade.
4. Shade the correct region.

Practice Problems

1. Graph the inequality \( y \geq 3x - 1 \).
2. Graph the inequality \( y \leq -x + 2 \).
3. Graph the inequality \( y > \frac{2}{3}x + 1 \).

Would you like further clarification on any of the steps or assistance with the practice problems?