To determine which equations or functions represent the graphed line, we need to analyze the slope and y-intercept of the line on the graph.

Step 1: Identifying Slope and Y-Intercept

1. The line crosses the y-axis at $y = -4$, so the y-intercept ($b$) is -4.
2. The line appears to rise by 1 unit for every 5 units it moves to the right, indicating a slope ($m$) of $\frac{1}{5}$.

Step 2: Equation of the Line

Using the slope-intercept form $y = mx + b$: $y = \frac{1}{5}x - 4$

Step 3: Match with Provided Options

Now, let’s check the options given:

1. Option 1: $f(x) = \frac{1}{5}x - 4$ — This matches our derived equation.
2. Other options should also have the same slope and y-intercept to represent the same line.

If you want further help with other options listed, feel free to provide the details of the remaining options, and I can verify each one.

Would you like additional details on identifying slope and intercepts?

Related Questions

1. What is the slope of a line, and how is it calculated from a graph?
2. How do you determine the y-intercept from a graph?
3. What is the slope-intercept form of a linear equation?
4. How do you convert between different forms of linear equations?
5. What steps can be taken to verify if a function represents a line on a graph?

Tip

To quickly check if an equation represents a graphed line, look for the slope and y-intercept in the equation and match them with the line’s features.