The inequality given is:

$y < 4x - 2$

To graph this inequality, we first look at the related linear equation:

$y = 4x - 2$

1. Find the y-intercept: The y-intercept is at $y = -2$, so the point $(0, -2)$ is on the line.
2. Find the slope: The slope is 4, which means for every 1 unit moved to the right (along the x-axis), we move up 4 units (along the y-axis). From the point $(0, -2)$, we can plot a second point by moving right 1 unit and up 4 units to reach the point $(1, 2)$.

Now, since the inequality is $y < 4x - 2$, the line is dashed (because the inequality does not include the equal sign). The shading is below the line, as $y$ values are less than the right-hand side of the equation.

Let's match this with the provided graphs:

• The first graph shows a shaded area above the line, which is incorrect for this inequality.
• The second graph shows a dashed line and shading below the line, which matches the inequality $y < 4x - 2$.
• The third graph shows shading above the line, which is also incorrect.

So, the second graph correctly represents the solution set for the inequality $y < 4x - 2$.

Would you like further explanation or more practice on inequalities? Here are some related questions:

1. How would the graph change if the inequality was $y \leq 4x - 2$?
2. How can you determine if a point is in the solution set of the inequality?
3. What is the difference between "strict" and "non-strict" inequalities in terms of graphing?
4. How would you graph the inequality $y \geq 2x + 3$?
5. Can you explain how to find the shading region for inequalities with a negative slope?

Tip: Always remember that dashed lines are used for strict inequalities (like $<$ or $>$), and solid lines are used for non-strict inequalities (like $\leq$ or $\geq$).