Question

graph the inequality $y \leq 11$.

Explanation:

Step1: Analyze the inequality

The inequality is \( y \leq 11 \). On a number line, for \( \leq \) or \( \geq \) inequalities, we use a closed (filled - in) circle at the boundary point because the point itself is included in the solution set. For \( < \) or \( > \) inequalities, we use an open circle. Here, since \( y \) can be equal to 11, we use a closed circle at 11.

Step2: Determine the direction of the line

The inequality \( y \leq 11 \) means that \( y \) can take any value less than or equal to 11. So, we draw a line starting from the closed circle at 11 and extending to the left (towards negative infinity or smaller numbers on the number line).

Answer:

To graph \( y\leq11 \):

1. Place a closed (filled - in) circle at \( y = 11 \) on the number line (because 11 is included in the solution set as the inequality is \( \leq \)).
2. Draw a line segment (or ray) starting from the closed circle at 11 and going to the left (towards values less than 11) to represent all the values of \( y \) that satisfy the inequality.