Question

which graph matches the inequality r ≥ -6? a) number line with a blue dot at -6 and arrow to the right b) number line with a blue dot at 4 and arrow to the right c) number line with an open circle at -6 and arrow to the right d) number line with an open circle at 4 and arrow to the left

Explanation:

Step1: Analyze the inequality \( r \geq -6 \)

The inequality \( r \geq -6 \) means we need a number line graph with a closed circle (since the inequality is "greater than or equal to") at \( -6 \) and the line shaded to the right (because \( r \) is greater than or equal to \( -6 \), so we include all values greater than or equal to \( -6 \)).

Step2: Evaluate each option

• Option A: The graph has a closed circle at \( -6 \) and is shaded to the right. This matches the inequality \( r \geq -6 \).
• Option B: The closed circle is at \( 4 \), not \( -6 \), so it does not match.
• Option C: The open circle is at \( -6 \) (open circle means \( r > -6 \), not \( r \geq -6 \)), so it does not match.
• Option D: The open circle is at \( 4 \), not related to \( -6 \), so it does not match.

Answer:

A. The graph with a closed circle at -6 and shaded to the right (the graph labeled A)