https://file.aiquickdraw.com/mathbot/file/1727192255259i3g04gjp.jpg

Let's analyze the information provided in the image and solve the problem step by step.

### Given:
- The linear function \( f(x) \) has a **y-intercept** of \( (0, 100) \).
- The **x-intercept** is \( (20, 0) \).

### Step 1: Find the slope of the line
The slope \( m \) of a line is calculated using two points on the line, using the slope formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \( (0, 100) \) and \( (20, 0) \):
\[
m = \frac{0 - 100}{20 - 0} = \frac{-100}{20} = -5
\]

### Step 2: Write the equation of the line
We use the slope-intercept form of a linear equation:

\[
f(x) = mx + b
\]
Where:
- \( m = -5 \) (from the slope we calculated).
- \( b = 100 \) (since the y-intercept is 100, \( f(0) = 100 \)).

Thus, the equation of the line is:

\[
f(x) = -5x + 100
\]

This matches the equation shown in the dropdown: \( f(x) = -5x + 100 \).

### Step 3: Interpretation of the Scenario
The next part of the question asks which scenario could be represented by this function. Without seeing the specific options for the scenarios in the dropdown menu, I can infer that \( f(x) = -5x + 100 \) represents a decreasing linear relationship (since the slope is negative). Possible scenarios might include things like a company losing money over time, or a tank draining water at a constant rate.

Would you like help interpreting a particular scenario or details on any other aspect?

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**Related Questions:**
1. How do we determine the y-intercept in a linear function?
2. What would change in the equation if the slope were positive?
3. How can you use two points to find the equation of any line?
4. What real-life scenarios are typically modeled by decreasing linear functions?
5. How does the slope affect the rate of change in a linear function?

**Tip:** Always double-check the intercepts when writing the equation of a line—they determine how the function behaves at key points.

Consider a linear function f(x) with a y-intercept of (0, 100) and an x-intercept of (20, 0). Select the equation for f(x). Which of the following scenarios could be represented by f(x)?

Solve a linear function problem with a y-intercept of (0, 100) and an x-intercept of (20, 0). Learn how to find the slope and write the equation of the line in slope-intercept form. Suitable for students in Grades 8-10.

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