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We are given the function \( f(x) = 5x - 8 \) and are tasked with filling in the table based on this function. The table already has \( f(-4) = -28 \) as shown in the example calculation:

\[
f(-4) = 5(-4) - 8 = -20 - 8 = -28
\]

Now, let's calculate the values for \( a \), \( b \), and \( c \) corresponding to \( f(-2) \), \( f(3) \), and \( f(7) \), respectively.

1. **For \( a = f(-2) \):**
\[
f(-2) = 5(-2) - 8 = -10 - 8 = -18
\]

2. **For \( b = f(3) \):**
\[
f(3) = 5(3) - 8 = 15 - 8 = 7
\]

3. **For \( c = f(7) \):**
\[
f(7) = 5(7) - 8 = 35 - 8 = 27
\]

Thus, the completed table should be:

| \( x \)  | \( f(x) \) |
|-------|----------|
| \( -4 \) | \( -28 \)  |
| \( -2 \) | \( -18 \)  |
| \( 3 \)  | \( 7 \)    |
| \( 7 \)  | \( 27 \)   |

So the values for the dropdowns are:
- \( a = -18 \)
- \( b = 7 \)
- \( c = 27 \)

Let me know if you'd like further explanation!

Here are 5 related questions to extend this problem:
1. How would the values change if the function were \( f(x) = 3x - 5 \)?
2. What is the slope of the function \( f(x) = 5x - 8 \)?
3. What does the \( -8 \) in the equation represent graphically?
4. How would you find the inverse of the function \( f(x) = 5x - 8 \)?
5. What is the domain and range of this linear function?

**Tip:** Always start by evaluating a function step by step to avoid mistakes, especially when dealing with negatives or complex expressions.

The table represents the function f(x) = 5x − 8. Find the values for the variables a, b, and c in the table based on the given function.

Learn how to evaluate the linear function f(x) = 5x - 8 by substituting given x-values. This example guides you through filling the table by calculating f(-2), f(3), and f(7) step-by-step. Suitable for students in Grades 8-10.

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