To determine the equation of the line in slope-intercept form, $y = mx + b$, let's analyze the line on the graph.

Step 1: Identify the Slope ($m$)

1. Choose two points on the line. From the image, we can see two clear points at:

   • Point 1: $(-8, 10)$
   • Point 2: $(4, 0)$

2. Calculate the slope $m$ using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Plugging in the values: $m = \frac{0 - 10}{4 - (-8)} = \frac{-10}{4 + 8} = \frac{-10}{12} = -\frac{5}{6}$

Step 2: Identify the Y-Intercept ($b$)

From the graph, the line crosses the y-axis at $y = 6$. Therefore, the y-intercept $b$ is 6.

Step 3: Write the Equation

Now that we have the slope $m = -\frac{5}{6}$ and the y-intercept $b = 6$, the equation of the line is: $y = -\frac{5}{6}x + 6$

Would you like a detailed explanation of each step, or do you have any questions?

Here are some related questions for practice:

1. How would you find the equation if the slope was positive instead?
2. What would change in the equation if the y-intercept was negative?
3. How do you find the slope if the coordinates are decimals instead of integers?
4. How would you rewrite the equation in standard form?
5. How do you interpret the slope of a line in real-life contexts?

Tip: Always ensure you double-check the slope and intercept points directly on the graph to avoid any small errors.