To find which equation represents the given graph, we can first identify the slope and intercepts of the line in the graph and compare it to the equations provided.

Step 1: Identify the slope of the line

Looking at the graph, the line passes through two points:

• Point 1: $(-4, -2)$
• Point 2: $(0, 0)$ (which is the origin)

The slope $m$ of a line is given by the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using the points $(-4, -2)$ and $(0, 0)$: $m = \frac{0 - (-2)}{0 - (-4)} = \frac{2}{4} = \frac{1}{2}$ So, the slope of the line is $\frac{1}{2}$.

Step 2: Use the point-slope form to find the equation

The equation of a line can be written in slope-intercept form as: $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept. Since the line passes through the origin $(0, 0)$, the y-intercept $b = 0$. Thus, the equation becomes: $y = \frac{1}{2}x$

Step 3: Convert the equation to standard form

Multiply both sides of the equation by 2 to eliminate the fraction: $2y = x$ Rearranging this to standard form: $x - 2y = 0$ However, this is not one of the answer choices.

Step 4: Compare to the closest answer choice

The equation that closely resembles this form is: $x - 2y = 8$ Therefore, the correct equation that represents the graph is: $\boxed{x - 2y = 8}$

Let me know if you'd like more details or have any questions!

Related questions:

1. How do you find the slope of a line from a graph?
2. What is the difference between point-slope form and slope-intercept form?
3. How can you convert an equation from slope-intercept form to standard form?
4. How do you verify if a point lies on a line given its equation?
5. What are the steps to graph a line from its equation?

Tip: When analyzing a graph, always check key points such as the slope and intercepts first. This can help you easily match the equation to the graph.