To solve and graph the inequality \( y + 4 \leq \frac{1}{2} \), we will follow these steps:
1. Isolate the variable \( y \):
- Start by isolating \( y \). Subtract 4 from both sides of the inequality to solve for \( y \).
[tex]\[
y + 4 \leq \frac{1}{2}
\][/tex]
[tex]\[
y \leq \frac{1}{2} - 4
\][/tex]
- Simplify the right-hand side:
[tex]\[
y \leq \frac{1}{2} - \frac{8}{2}
\][/tex]
[tex]\[
y \leq -\frac{7}{2}
\][/tex]
[tex]\[
y \leq -3.5
\][/tex]
2. Create the Graph:
- Draw a horizontal line on the graph where \( y = -3.5 \). This line represents the boundary of the inequality.
- Since the inequality symbol is \( \leq \), we include the line \( y = -3.5 \) in the solution set. Thus, we draw a solid line.
- To indicate the region where the inequality holds, shade the area below the line \( y = -3.5 \). This represents all the points where \( y \) is less than or equal to \(-3.5\).
3. Match the Graph:
- Look at each of the provided answer choices (Graph A, B, C, and D).
- The correct graph will have a solid horizontal line at \( y = -3.5 \) and will shade the region below this line.
Based on the given information and the proper steps, identify the graph that has a solid line at \( y = -3.5 \) with shading below it.
Find and select the correct choice that matches this description:
- A. Graph A
- B. Graph B
- C. Graph C
- D. Graph D
By carefully analyzing the graphs, you will find the one that correctly represents the inequality \( y + 4 \leq \frac{1}{2} \):
Determine the correct graph by looking for a solid line at [tex]\( y = -3.5 \)[/tex] with shading below it.
