To graph the inequality \( y > 4x - 2 \) on a coordinate plane, follow these steps:

1. **Start by graphing the boundary line**: The boundary for this inequality is the line \( y = 4x - 2 \). This line is where \( y \) equals \( 4x - 2 \). To graph it:
   - Choose two values of \( x \), and calculate the corresponding \( y \) values.
     - For \( x = 0 \), \( y = 4(0) - 2 = -2 \) (Point: \( (0, -2) \))
     - For \( x = 1 \), \( y = 4(1) - 2 = 2 \) (Point: \( (1, 2) \))
   - Plot these points on the coordinate plane and draw the line that passes through them.
   - Use a **dashed line** because the inequality is strict ("greater than" but not "equal to"), so points on the line itself are **not included** in the solution.

2. **Shade the region above the line**: The inequality is \( y > 4x - 2 \), meaning you want the region where \( y \) is greater than the value of \( 4x - 2 \). To do this:
   - Pick a test point that is not on the line, such as \( (0, 0) \).
   - Substitute \( x = 0 \) and \( y = 0 \) into the inequality: \( 0 > 4(0) - 2 \Rightarrow 0 > -2 \), which is true.
   - Since the point \( (0, 0) \) satisfies the inequality, shade the region above the dashed line.

This shaded region represents all the points where \( y \) is greater than \( 4x - 2 \).

Would you like a more detailed explanation or help with another graphing concept?

Here are 5 questions that expand on this topic:
1. How do you graph inequalities with different slopes?
2. How does shading change if the inequality symbol is "less than" instead of "greater than"?
3. What does the graph look like if the inequality were \( y \geq 4x - 2 \) instead of \( y > 4x - 2 \)?
4. How do you graph inequalities involving vertical or horizontal lines?
5. How would the graph change if the slope of the line was negative?

**Tip**: Always use a dashed line for inequalities that are "strict" (e.g., \( < \) or \( > \)) and a solid line for "inclusive" inequalities (e.g., \( \leq \) or \( \geq \)).

Learn how to graph the inequality y > 4x - 2 step by step. This tutorial covers graphing linear inequalities, plotting boundary lines, and shading the correct region. Perfect for students in Grades 8-10 studying algebra and inequalities.

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