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I need help on this. I’ve looked everywhere but seemed that I can’t grasp this how to determine where to shade

It looks like you're working with inequalities, specifically \( y > 4x - 2 \), and you're asking about how to determine where to shade on a graph. Let me explain how to graph this inequality and where to shade.

### Steps to Graph \( y > 4x - 2 \):

1. **Start with the equation of the boundary line**: 
   - Treat the inequality as if it were an equation, \( y = 4x - 2 \). This is the boundary line. It has a slope of 4 and a y-intercept of -2. 

2. **Plot the boundary line**:
   - The y-intercept is -2, so start by plotting the point \( (0, -2) \) on the graph.
   - The slope is 4, which means for every 1 unit you move to the right, you move 4 units up. Plot another point using this slope, like \( (1, 2) \).
   - Now, draw the boundary line. Since the inequality is \( y > 4x - 2 \), **use a dashed line** because the points on the line are **not** included in the solution (the inequality is strict: "greater than," not "greater than or equal to").

3. **Determine where to shade**:
   - To figure out which side of the line to shade, choose a test point that is not on the boundary line. A good point to use is the origin, \( (0, 0) \).
   - Plug the test point into the inequality:
     \[
     0 > 4(0) - 2 \implies 0 > -2
     \]
   - This is a true statement, so the region that includes \( (0, 0) \) should be shaded.
   
4. **Shading**:
   - Since \( (0, 0) \) satisfies the inequality, shade **above** the boundary line, because the inequality is \( y > 4x - 2 \). If the inequality had been \( y < 4x - 2 \), you would shade below the line.

Would you like any further details on this? Here are some follow-up questions to help deepen your understanding:

1. How do you plot points using the slope-intercept form of a line?
2. What changes if the inequality were \( y \geq 4x - 2 \) instead?
3. How would you test if a point lies on the boundary line?
4. What other test points can you use to verify the shading?
5. How do you handle vertical or horizontal lines when graphing inequalities?

**Tip:** When working with inequalities, always remember that a dashed line represents a strict inequality ( \( < \) or \( > \) ), while a solid line represents inclusive inequalities ( \( \leq \) or \( \geq \) ).

Learn how to graph the linear inequality y > 4x - 2 and determine the correct region to shade. This problem covers graphing concepts, including boundary lines, test points, and the difference between strict and inclusive inequalities.

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