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The problem asks to write a linear function \( g \) using the given points:

- \( g(0) = 9 \) (which means the y-intercept is 9),
- \( g(8) = 7 \) (which gives the point \( (8, 7) \)).

### Step-by-step solution:

1. **Identify the form of the linear function:**

   A linear function can be written as:
   \[
   g(x) = mx + b
   \]
   where \( m \) is the slope and \( b \) is the y-intercept.

2. **Use the point \( g(0) = 9 \) to find the y-intercept \( b \):**

   Since \( g(0) = 9 \), we know that \( b = 9 \).

   So the equation becomes:
   \[
   g(x) = mx + 9
   \]

3. **Find the slope \( m \) using the points \( (0, 9) \) and \( (8, 7) \):**

   The slope formula is:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   Substituting \( (x_1, y_1) = (0, 9) \) and \( (x_2, y_2) = (8, 7) \):
   \[
   m = \frac{7 - 9}{8 - 0} = \frac{-2}{8} = -\frac{1}{4}
   \]

4. **Write the final equation:**

   Now that we know the slope \( m = -\frac{1}{4} \) and the y-intercept \( b = 9 \), the linear function is:
   \[
   g(x) = -\frac{1}{4}x + 9
   \]

### Final Answer:
The linear function is:
\[
g(x) = -\frac{1}{4}x + 9
\]

Would you like further details on the steps or explanation? Here are 5 related questions to deepen your understanding:

1. How do we know that the slope is negative in this case?
2. Why is the point \( g(0) = 9 \) called the y-intercept?
3. How can we verify that \( g(x) = -\frac{1}{4}x + 9 \) passes through \( (8, 7) \)?
4. What happens if the slope is 0 in a linear equation?
5. How would the equation change if the slope were positive instead?

**Tip:** When finding the slope, always subtract in the same order for both coordinates to avoid sign mistakes!

Write a linear function g with the given values: g(0) = 9, g(8) = 7. Show your work.

Learn how to find the equation of a linear function given the points (0, 9) and (8, 7). This problem focuses on slope-intercept form and calculating the slope between two points. Suitable for students in Grades 8-10.

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