https://file.aiquickdraw.com/mathbot/file/17266772169213c3lfins.jpg

The graph shows a straight line, and the task is to determine the equation of the function \( f(x) \) that matches the graph.

### To determine the equation:
The general equation of a straight line is:
\[
f(x) = mx + b
\]
where:
- \( m \) is the slope (Steigung),
- \( b \) is the y-intercept (y-Achsenabschnitt).

#### Step 1: Find the slope \( m \)
The slope \( m \) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
From the graph:
- One point is \( (0, 4) \) (the y-intercept).
- Another point is \( (2, 0) \) (where the line crosses the x-axis).

Using these points:
\[
m = \frac{0 - 4}{2 - 0} = \frac{-4}{2} = -2
\]

#### Step 2: Find the y-intercept \( b \)
The y-intercept \( b \) is where the line crosses the y-axis. From the graph, this is \( b = 4 \).

#### Final Equation
So, the equation of the line is:
\[
f(x) = -2x + 4
\]

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How do you calculate the slope of a line when given two points?
2. What is the significance of the y-intercept in a linear function?
3. How would the graph change if the slope were positive?
4. Can you determine the x-intercept from the equation of the line?
5. How do you graph a linear equation using just the slope and y-intercept?

**Tip:** The slope indicates the direction of the line. A negative slope means the line descends from left to right.

Geben Sie zum abgebildeten Funktionsgraph eine passende Funktionsgleichung an. Der Graph zeigt eine Gerade, die von Punkt (0, 4) bis Punkt (2, 0) verläuft.

Learn how to find the equation of a line from a graph with points (0, 4) and (2, 0). This lesson covers calculating the slope, identifying the y-intercept, and writing the equation in slope-intercept form. Ideal for students in Grades 8-10.

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