https://file.aiquickdraw.com/mathbot/file/1725973261125cn1nr6u1.jpg

To calculate the rate of change (slope) of the line through the two points shown on the graph, we'll use the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\):

\[
\text{slope (m)} = \frac{y_2 - y_1}{x_2 - x_1}
\]

From the graph, the two points where the line crosses are approximately:

- \((0, 4)\)
- \((4, 0)\)

Now, applying the formula:

\[
m = \frac{0 - 4}{4 - 0} = \frac{-4}{4} = -1
\]

So, the rate of change (slope) of the line is **-1**.

Would you like more details or have any further questions?

Here are 5 related questions for deeper exploration:
1. How does the slope of a line relate to its steepness?
2. What would the slope be if the line was horizontal?
3. How can you calculate the slope if given an equation of a line?
4. What does a positive slope indicate compared to a negative slope?
5. Can you find the slope of a line without using a graph?

**Tip:** The slope of a line represents the rate at which the \(y\)-coordinate changes with respect to the \(x\)-coordinate.

Calculate the rate of change of a line through the 2 points.

Learn how to calculate the rate of change (slope) of a line through two points on a graph using the slope formula. This problem covers key algebraic concepts including linear equations and the slope theorem. Suitable for students in Grades 7-9.

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