https://file.aiquickdraw.com/mathbot/file/17298124287051da3fj7z.jpg

Let's analyze the problem in the image. We are given two linear functions:

- **Function A** is represented by the graph.
- **Function B** is given as \( y = \frac{1}{2}x - 5 \).

### Step 1: Slope Comparison

- **Function A:** By observing the graph, the line crosses the y-axis at \( y = -3 \), and we can calculate the slope by using the rise-over-run method. The line appears to go up by 2 units (rise) when moving 1 unit to the right (run), indicating a slope of **2**.
  
- **Function B:** The slope can be directly taken from the equation \( y = \frac{1}{2}x - 5 \), which is \( \frac{1}{2} \).

Thus, the slope of **Function A** (2) is greater than the slope of **Function B** (\( \frac{1}{2} \)).

### Step 2: Checking y-values when \( x = 4 \)

- **For Function A:** Using the graph, we can estimate that when \( x = 4 \), the corresponding \( y \)-value is around 5.
  
- **For Function B:** Plugging \( x = 4 \) into the equation:
  \[
  y = \frac{1}{2}(4) - 5 = 2 - 5 = -3
  \]
  So, when \( x = 4 \), the \( y \)-value for Function B is \( -3 \).

### Step 3: Statement Verification

1. **"The slope of Function A is less than the slope of Function B."**  
   This is **false** because the slope of Function A (2) is greater than that of Function B (\( \frac{1}{2} \)).

2. **"The slope of Function A is equal to the slope of Function B."**  
   This is **false** because 2 is not equal to \( \frac{1}{2} \).

3. **"The y-value of Function A when \( x = 4 \) is equal to the y-value of Function B when \( x = 4 \)."**  
   This is **false** because Function A gives \( y \approx 5 \) while Function B gives \( y = -3 \).

4. **"The y-value of Function A when \( x = 4 \) is greater than the y-value of Function B when \( x = 4 \)."**  
   This is **true** because 5 is greater than -3.

### Correct Answer:

The only true statement is:
- The y-value of Function A when \( x = 4 \) is greater than the y-value of Function B when \( x = 4 \).

Would you like a more detailed explanation or have any further questions?

Here are 5 related questions to expand your understanding:
1. How do you calculate the slope from a graph of a line?
2. What does the slope tell us about the steepness of a line?
3. How would you graph \( y = \frac{1}{2}x - 5 \) without using a calculator?
4. How can you determine the y-intercept from the graph of Function A?
5. How would the graph of Function A change if its slope were negative?

**Tip:** When comparing functions, always check both the slope and the y-intercept to fully understand the differences in their behavior.

Analyze and verify statements about two linear functions. Function A is represented by a graph, and Function B is defined as y = (1/2)x - 5.

Explore the comparison between two linear functions: one represented graphically and the other by the equation y = (1/2)x - 5. This problem involves calculating slopes, checking y-values at specific x-values, and verifying statements about function behavior. Suitable for students in Grades 8-10.

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