To graph the linear inequality $y > 2x - 4$, follow these steps:

1. Graph the Boundary Line:

   • Rewrite the inequality as an equation: $y = 2x - 4$.
   • This line has a slope of 2 and a y-intercept of -4. Plot the point (0, -4) on the y-axis.
   • Use the slope to plot another point: since the slope is 2, go up 2 units and right 1 unit from (0, -4) to get a second point.
   • Draw a dashed line through these points because the inequality is strictly greater than (>) and does not include equality (not $y \geq 2x - 4$).

2. Shade the Appropriate Region:

   • Since the inequality is $y > 2x - 4$, shade the region above the line, where $y$-values are greater than those on the line.

The dashed line indicates points that are not included in the solution, and the shaded area above the line represents all points $(x, y)$ that satisfy $y > 2x - 4$.

Would you like further details on this process or have any questions?

Here are some related questions that might interest you:

1. How do you graph inequalities that involve $\leq$ or $\geq$?
2. What changes if the inequality is $y < 2x - 4$?
3. How can you find points that satisfy the inequality directly?
4. What if the inequality involves a different slope or intercept?
5. How would you check if a particular point satisfies $y > 2x - 4$?

Tip: Always use a dashed line for ">" or "<" inequalities and a solid line for "≥" or "≤" inequalities.