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.