To determine the rate of change (slope) from the graph provided, we can follow these steps:

Step 1: Identify two points on the line

From the image, two clear points on the line appear to be:

• Point 1: $(-5, 4)$
• Point 2: $(5, -4)$

Step 2: Use the slope formula

The slope (rate of change) $m$ is given by:

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

Plugging in the coordinates from the two points:
$(x_1, y_1) = (-5, 4)$ and $(x_2, y_2) = (5, -4)$:

$m = \frac{-4 - 4}{5 - (-5)} = \frac{-8}{10} = -\frac{4}{5}$

Step 3: Interpret the result

The rate of change (slope) of the function is $-\frac{4}{5}$.

So, the correct answer is:

$-\frac{4}{5}$

Let me know if you want more details or have any questions!

Here are 5 related questions to deepen your understanding:

1. What does a negative slope indicate about the direction of a line?
2. How can you tell if two lines are parallel based on their slopes?
3. What would the slope be if the line were horizontal?
4. If a line passes through the origin, how does its slope affect the y-intercept?
5. How would the slope change if we switched the points in the slope calculation?

Tip: Remember, slope tells us how much the y-value changes for a given change in x. It helps describe the "steepness" of a line.