The image shows a problem related to graphing the solution set of a system of linear inequalities. The inequalities provided in the screenshot are:

$2y - 2x > 8 \quad \text{or} \quad y > 2$

Step-by-step breakdown:

1. Inequality 1: $2y - 2x > 8$:

   • First, solve for $y$ in terms of $x$: $2y > 2x + 8$ $y > x + 4$
   • This is the equation of a line: $y = x + 4$, but since the inequality is $y > x + 4$, you will graph the line $y = x + 4$ and shade above it.
   • The boundary line should be dashed because it is a strict inequality (no equal sign, meaning the line itself is not part of the solution).

2. Inequality 2: $y > 2$:

   • This is a horizontal line at $y = 2$, and since the inequality is $y > 2$, you will shade the region above this line.
   • The boundary line for this inequality is also dashed because it is a strict inequality.

Graphing Instructions:

• For the first inequality $y = x + 4$, you can find two points on the line by substituting values for $x$ to solve for $y$.
  • For $x = 0$, $y = 4$ (point: $(0, 4)$).
  • For $x = -4$, $y = 0$ (point: $(-4, 0)$).
• For the second inequality $y = 2$, the points on the line are easy to determine as they are horizontal at $y = 2$ (e.g., $(-10, 2)$, $(10, 2)$).

In summary:

• For the boundary line $y = x + 4$, enter the points $(0, 4)$ and $(-4, 0)$.
• Choose a dashed boundary for both inequalities since they are strict inequalities.

Would you like me to explain anything further or assist with entering the points?

Follow-up questions:

1. Why is the boundary line dashed for a strict inequality?
2. How would the solution change if the inequality was $y \geq x + 4$?
3. How do we determine which region to shade in a graph of inequalities?
4. Can you graph systems with more than two inequalities in this manner?
5. What role does the slope of the line play in understanding the graph?

Tip:

Always test a point (like $(0, 0)$) to check whether it belongs to the solution set when graphing inequalities.