Question

Question was provided via image upload.

Explanation:

To graph the solution set of the inequality \( y > 2 \) on the number line:

Step 1: Identify the critical point

The solution to the inequality is \( y > 2 \). This means the critical point is \( 2 \).

Step 2: Determine the type of circle

Since the inequality is \( y > 2 \) (not \( y \geq 2 \)), we use an open circle at \( 2 \) to indicate that \( 2 \) is not included in the solution set.

Step 3: Determine the direction of the arrow

Because \( y \) must be greater than \( 2 \), the arrow on the number line should point to the right (towards the positive, larger numbers) from the open circle at \( 2 \).

To draw this:

1. Locate \( 2 \) on the number line.
2. Draw an open circle at \( 2 \).
3. Draw an arrow starting from the open circle at \( 2 \) and pointing to the right (towards \( 3, 4, 5, \dots \)).

The graph will have an open circle at \( 2 \) and an arrow extending to the right.

Answer:

To graph the solution set of the inequality \( y > 2 \) on the number line:

Step 1: Identify the critical point

The solution to the inequality is \( y > 2 \). This means the critical point is \( 2 \).

Step 2: Determine the type of circle

Since the inequality is \( y > 2 \) (not \( y \geq 2 \)), we use an open circle at \( 2 \) to indicate that \( 2 \) is not included in the solution set.

Step 3: Determine the direction of the arrow

Because \( y \) must be greater than \( 2 \), the arrow on the number line should point to the right (towards the positive, larger numbers) from the open circle at \( 2 \).

To draw this:

1. Locate \( 2 \) on the number line.
2. Draw an open circle at \( 2 \).
3. Draw an arrow starting from the open circle at \( 2 \) and pointing to the right (towards \( 3, 4, 5, \dots \)).

The graph will have an open circle at \( 2 \) and an arrow extending to the right.