From the image, we can determine the equation of the line in slope-intercept form ($y = mx + b$) by analyzing the graph. Here's how:

1. Identify the slope ($m$):

   • Pick two points on the line. From the graph:
     • Point 1: $(-6, 5)$
     • Point 2: $(0, 1)$
   • Calculate the slope using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$: $m = \frac{1 - 5}{0 - (-6)} = \frac{-4}{6} = -\frac{2}{3}.$

2. Determine the y-intercept ($b$):

   • The y-intercept is where the line crosses the y-axis. From the graph, this occurs at $(0, 1)$. Thus, $b = 1$.

3. Write the equation:

   • Substitute $m = -\frac{2}{3}$ and $b = 1$ into the slope-intercept form: $y = -\frac{2}{3}x + 1.$

Final Answer:

The equation of the line is: $y = -\frac{2}{3}x + 1.$

Would you like me to explain any part of the process further or analyze another problem?

Expansion Questions:

1. How is the slope of a line determined from two points?
2. What are the key steps to writing an equation in slope-intercept form?
3. How can you check if your slope calculation is correct?
4. Why is the y-intercept important in defining a linear equation?
5. How would this equation change if the line were steeper?

Tip:

Always double-check your slope by ensuring the direction of the line (positive or negative) matches your calculation!