To find the rate of change represented by the graph, we can calculate the slope of the line using two given points. From the image, the points on the line are:

• $(-4, -6)$
• $(4, -2)$

Step 1: Apply the slope formula

The slope $m$ (rate of change) between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

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

Step 2: Substitute the values

Using $(x_1, y_1) = (-4, -6)$ and $(x_2, y_2) = (4, -2)$:

$m = \frac{-2 - (-6)}{4 - (-4)}$

Step 3: Simplify

$m = \frac{-2 + 6}{4 + 4} = \frac{4}{8} = \frac{1}{2}$

Final Answer

The rate of change (or slope) of the graph is:

$m = \frac{1}{2}$

This means that for every 2 units increase in $x$, $y$ increases by 1 unit.

Would you like further details on slope or have any questions?

Here are five related questions to expand your understanding:

1. What does a negative slope represent in a graph?
2. How do you find the slope if the line is vertical or horizontal?
3. What is the equation of a line with slope $1/2$ passing through $(4, -2)$?
4. How can you use the slope-intercept form $y = mx + b$ for this line?
5. How is the rate of change related to real-world problems, such as speed?

Tip: Always check if the line passes through the origin (0,0) to make slope calculations quicker!