To determine the equation of the line in the graph, we need to find two key components:

1. Slope (m): The slope of the line can be determined by identifying two points on the line and applying the slope formula:

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

2. y-intercept (b): The y-intercept is the point where the line crosses the y-axis.

Step 1: Identify two points

Looking at the graph, two points on the line are:

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

Step 2: Calculate the slope (m)

Using the slope formula:

$m = \frac{-8 - 8}{8 - (-10)} = \frac{-16}{18} = -\frac{8}{9}$

So, the slope $m = -\frac{8}{9}$.

Step 3: Find the y-intercept (b)

The y-intercept occurs when $x = 0$. From the graph, the line crosses the y-axis at approximately $b = 0$.

Final Equation of the Line:

Now that we have the slope $m = -\frac{8}{9}$ and the y-intercept $b = 0$, the equation of the line is:

$y = -\frac{8}{9}x$

Would you like more details on any step, or do you have any questions?

Here are 5 related questions to explore further:

1. What does the slope tell you about the direction of the line?
2. How would the equation change if the y-intercept were different?
3. Can the slope formula be applied to vertical lines? Why or why not?
4. What is the significance of a zero y-intercept in this equation?
5. How can you graph a line using just the slope and the y-intercept?

Tip: A negative slope always indicates that the line is decreasing as it moves from left to right.