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 $\geq$ ).