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The graph presented shows a linear function. To determine which of the four equations corresponds to this graph, we need to analyze two key properties: **slope** and **y-intercept**.

1. **Slope**: The line is rising as it moves from left to right, which indicates a **positive slope**.
2. **Y-intercept**: The line crosses the y-axis at **-4**.

The equation of a straight line is generally written in slope-intercept form, \( y = mx + b \), where \( m \) is the slope, and \( b \) is the y-intercept.

- From the graph, the y-intercept is clearly **-4**.
- Looking at the slope, the line rises 2 units for every 1 unit it moves horizontally, suggesting the slope \( m = \frac{1}{2} \).

Given this information, the correct equation of the line is:

\[
y = \frac{1}{2}x - 4
\]

Thus, the correct choice is the last equation: **\( y = \frac{1}{2}x - 4 \)**.

Would you like further details or have any questions?

Here are 5 related questions:
1. What does the slope of a line represent?
2. How do you find the slope from a graph?
3. How does the sign of the slope affect the direction of the line?
4. What is the significance of the y-intercept in a linear equation?
5. How can you rewrite the equation \( y = \frac{1}{2}x - 4 \) in standard form?

**Tip:** The slope tells you how steep a line is; it’s the ratio of the vertical change to the horizontal change between two points on the line.

Which function is represented by the graph below?

Learn how to determine which linear function corresponds to the graph, focusing on slope-intercept form. Analyze the slope and y-intercept to solve this algebra problem. Suitable for Grades 8-10.

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