To determine the equation of the line, we need to identify the slope $m$ and the y-intercept $c$ from the graph. Here's how we can approach it:

1. Find the slope $m$: The slope is calculated by determining how much the line rises or falls for each unit it moves horizontally. We can pick two points on the line, for instance, (x1, y1) and (x2, y2), and use the slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ By selecting two points on the graph, we can calculate the slope.

2. Find the y-intercept $c$: This is the point where the line crosses the y-axis. From the graph, we can observe this point.

Let me check the graph and calculate the slope and intercept. PIL import Image

Open the image to analyze it

image_path = '/mnt/data/1740936079995znftafre.jpg' img = Image.open(image_path) img.show()I've opened the image of the graph. Now, I'll analyze the line to find two key points and calculate the slope and y-intercept.

I'll proceed with extracting the slope and y-intercept from the graph.Based on the graph:

• The line intersects the y-axis at $y = -8$, so the y-intercept $c = -8$.
• For the slope $m$, let's calculate the rise over run between two points on the line. One point is at $(-4, -4)$ and the other is at $(4, 4)$.

Using the slope formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the points $(-4, -4)$ and $(4, 4)$:

$m = \frac{4 - (-4)}{4 - (-4)} = \frac{8}{8} = 1$

Thus, the slope is $m = 1$.

Therefore, the equation of the line is: $y = x - 8$

Let me know if you'd like any further details or clarifications! Here's a list of related questions:

1. How do you calculate the slope when the graph is not a straight line?
2. How do we interpret the slope in real-world contexts?
3. How can we write the equation of a line in other forms, like point-slope form?
4. What are some real-world examples of lines with a slope of 1?
5. How does the y-intercept relate to the line’s position on the graph?

Tip: Always ensure to choose points clearly aligned with the grid to minimize errors when calculating the slope.