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You provided an image of a table related to the function \( f(x) = -3x + 23 \). The table lists several values of \( x \) (5, 7, 8, 9, 10) and asks for the corresponding values of \( f(x) \).

Let's calculate each \( f(x) \) value for the given \( x \)-values.

The formula is:
\[
f(x) = -3x + 23
\]

1. For \( x = 5 \):
\[
f(5) = -3(5) + 23 = -15 + 23 = 8
\]

2. For \( x = 7 \):
\[
f(7) = -3(7) + 23 = -21 + 23 = 2
\]

3. For \( x = 8 \):
\[
f(8) = -3(8) + 23 = -24 + 23 = -1
\]

4. For \( x = 9 \):
\[
f(9) = -3(9) + 23 = -27 + 23 = -4
\]

5. For \( x = 10 \):
\[
f(10) = -3(10) + 23 = -30 + 23 = -7
\]

Now the completed table would look like:

| \( x \) | \( f(x) \) |
|--------|------------|
| 5      | 8          |
| 7      | 2          |
| 8      | -1         |
| 9      | -4         |
| 10     | -7         |

Would you like more details or have any questions on these calculations?

Here are some relative questions:
1. How do you derive the slope of the function \( f(x) \)?
2. What happens to \( f(x) \) as \( x \) increases?
3. How would you graph this function based on the table values?
4. What is the y-intercept of the function \( f(x) = -3x + 23 \)?
5. Can you think of any real-life examples where a linear function like this might be useful?

**Tip**: Remember, the coefficient of \( x \) in a linear equation like \( f(x) = -3x + 23 \) represents the slope, which tells you the rate of change of the function.

Complete the table for f(x) = -3x + 23 for the values of x (5, 7, 8, 9, 10).

Learn how to solve the linear function f(x) = -3x + 23 by calculating f(x) for x = 5, 7, 8, 9, and 10. This exercise focuses on linear functions, slope-intercept form, and algebra, suitable for students in Grades 6-8.

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