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The problem presents two linear functions, Function A and Function B. Function A is represented by a graph, and Function B is given by a table of values. The question asks to compare the \(y\)-values of the two functions when \(x = -5\).

Let's analyze each function:

### Function A (Graph):
To determine the \(y\)-value of Function A when \(x = -5\), locate \(x = -5\) on the graph of Function A. By observing the graph, when \(x = -5\), the corresponding \(y\)-value is about **-5**.

### Function B (Table):
For Function B, the table provides the following values:
- When \(x = -10\), \(y = -3\)
- When \(x = 5\), \(y = 0\)
- When \(x = 10\), \(y = 1\)

We need to calculate or interpolate the \(y\)-value for \(x = -5\) based on the given data. The slope of Function B can be found using any two points. Let's use \((5, 0)\) and \((10, 1)\).

The slope \(m\) is calculated as:
\[
m = \frac{1 - 0}{10 - 5} = \frac{1}{5}
\]
Now we use the slope formula \(y = mx + b\) to find the equation of Function B. Since the point \((5, 0)\) is on the line, we can substitute it into the equation to find the y-intercept \(b\):
\[
0 = \frac{1}{5}(5) + b \implies b = -1
\]
So, the equation of Function B is:
\[
y = \frac{1}{5}x - 1
\]

Now, substitute \(x = -5\) into the equation:
\[
y = \frac{1}{5}(-5) - 1 = -1 - 1 = -2
\]

### Comparison:
- For Function A, \(y = -5\) when \(x = -5\).
- For Function B, \(y = -2\) when \(x = -5\).

### Conclusion:
The \(y\)-value of Function A when \(x = -5\) is less than the \(y\)-value of Function B at \(x = -5\). Therefore, the correct statement is:
- "The \(y\)-value of Function A when \(x = -5\) is less than the \(y\)-value of Function B when \(x = -5\)."

Would you like more details or have any questions?

Here are five related questions to explore:
1. How do you calculate the slope of a line given two points?
2. What is the significance of the slope and y-intercept in the equation of a line?
3. How would the graph of Function B look based on its equation?
4. How can you solve for the \(y\)-value at any given \(x\) using a function’s equation?
5. What is the general form of a linear function and how does it relate to real-world problems?

**Tip:** When comparing two functions, always check if they are linear and use their slope and intercept to determine how they behave at specific values of \(x\).

Compare the y-values of Function A and Function B when x = -5.

Learn how to compare the y-values of two linear functions, one represented by a graph and the other by a table of values. This step-by-step solution helps students analyze and solve the problem for x = -5. Suitable for Grades 8-10.

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