https://file.aiquickdraw.com/mathbot/file/1727418347905p4oqlpwl.jpg

The image shows a graph with a blue line, and the question asks for the gradient (slope) of that line. To calculate the gradient of a line, we use the formula:

\[
\text{Gradient} = \frac{{\text{change in } y}}{{\text{change in } x}} = \frac{{y_2 - y_1}}{{x_2 - x_1}}
\]

From the graph, I can see two points on the line:
- One point is \((-5, 3)\)
- Another point is \((5, -2)\)

Now, let's calculate the gradient:

\[
\text{Gradient} = \frac{{-2 - 3}}{{5 - (-5)}} = \frac{{-5}}{{5 + 5}} = \frac{{-5}}{{10}} = -\frac{1}{2}
\]

So, the gradient of the blue line is \(-\frac{1}{2}\).

Do you want more details or have any questions? Here are 5 related questions to deepen your understanding:

1. How does the slope of a line affect its direction?
2. What is the gradient of a horizontal line?
3. How would the gradient change if the points on the line were swapped?
4. Can two different lines have the same gradient? If yes, what does that imply?
5. How do you find the y-intercept using the gradient and one point on the line?

**Tip**: The gradient gives an indication of the steepness and direction of the line—negative gradients slope downwards from left to right.

Learn how to calculate the gradient (slope) of a line given a graph. This problem uses the formula for gradient, focusing on key points (x1, y1) and (x2, y2) from the graph. Suitable for students in Grades 8-10.

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