To write the equation of the line in slope-intercept form, we need to determine the slope and the y-intercept from the graph.

Step 1: Identify two points on the line

From the graph, we can see that the line passes through the points:

• $(-8, 7)$
• $(4, -5)$

Step 2: Calculate the slope (m)

The slope is calculated as: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using the points $(-8, 7)$ and $(4, -5)$: $m = \frac{-5 - 7}{4 - (-8)} = \frac{-12}{12} = -1$

Step 3: Find the y-intercept (b)

The slope-intercept form is: $y = mx + b$ Using the slope $m = -1$ and one of the points (I'll use $(4, -5)$) to solve for $b$: $-5 = -1(4) + b$ $-5 = -4 + b$ $b = -5 + 4 = -1$

Step 4: Write the equation

Now that we know $m = -1$ and $b = -1$, the equation of the line is: $y = -x - 1$

Would you like further details on any part of this process?

Here are 5 related questions to deepen your understanding:

1. How would the equation change if the slope were positive?
2. What is the significance of the y-intercept in a real-world context?
3. How can you find the equation of a vertical or horizontal line?
4. What are the implications of a slope of 0 or undefined in a graph?
5. How would you graph a line if only given the slope and a point?

Tip: Always double-check that the points you select for calculating the slope are accurate on the graph to avoid calculation errors.