Graphing an Inequality on a Number Line
The inequality given in the image is \( t \geq -3 \). To graph this inequality on a number line:
1. Locate the point -3 on the number line.
2. Since the inequality includes "greater than or equal to" (as indicated by the symbol \(\geq\)), you need a solid circle or dot at -3. This shows that -3 is part of the solution set.
3. Shade the number line to the right of -3, indicating all numbers greater than -3 are also included in the solution set.
Now let's examine the provided options to see which graph corresponds to these instructions:
A. This graph shows a number line with a solid dot at -3 and shading towards the left, which means values less than -3. This does not match the inequality.
B. This graph shows a number line with an open circle at -3 (indicating that -3 is not included) and shading towards the right. This is not correct because the inequality specifies that -3 is included.
C. This graph shows a number line with a solid dot at -3 and shading to the right, which seems to match the inequality \( t \geq -3 \).
D. This graph depicts a number line with a solid dot at 3 and shading to the right; however, this does not correspond to the inequality provided.
The correct answer is C, as it correctly represents the inequality \( t \geq -3 \).
