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.