The task asks for the equation of the line in slope-intercept form, which is written as:

$y = mx + b$

where $m$ is the slope of the line, and $b$ is the y-intercept (where the line crosses the y-axis).

Step 1: Find the Slope (m)

The slope $m$ is calculated using the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Looking at the graph, I can pick two points on the line:

• Point 1: $(-8, -7)$
• Point 2: $(4, 3)$

Now, let's compute the slope:

$m = \frac{3 - (-7)}{4 - (-8)} = \frac{3 + 7}{4 + 8} = \frac{10}{12} = \frac{5}{6}$

So, the slope $m$ is $\frac{5}{6}$.

Step 2: Find the Y-Intercept (b)

The y-intercept $b$ is the point where the line crosses the y-axis. From the graph, it can be seen that the line crosses the y-axis at $y = -\frac{5}{6}$.

Final Equation

The equation of the line in slope-intercept form is:

$y = \frac{5}{6}x - \frac{5}{6}$

Would you like further clarification on any part of the solution?

Here are five related questions you might explore:

1. How would the equation change if the line had a steeper slope?
2. How can we derive the equation if we are given just the slope and a point on the line?
3. What is the significance of the y-intercept in real-world problems?
4. How do horizontal and vertical lines look in slope-intercept form?
5. How would you find the equation if the slope was negative?

Tip: When finding the slope of a line, always ensure to carefully choose points that lie exactly on grid intersections for accuracy.