https://file.aiquickdraw.com/mathbot/file/1727418283584thp82kcv.jpg

To find the gradient (slope) of the blue line from the image, we can use the formula for the gradient:

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

From the image, the blue line appears to pass through the following two points:
- Point 1: \((0, 0)\) 
- Point 2: \((3, 2)\)

Using these points:

\[
m = \frac{2 - 0}{3 - 0} = \frac{2}{3}
\]

Thus, the gradient of the blue line is **\(\frac{2}{3}\)**.

Would you like further explanation or details?

Here are 5 related questions to expand your understanding:
1. How do you calculate the gradient of a vertical line?
2. What does a negative gradient indicate about a line's direction?
3. How can you calculate the equation of a line if you know the gradient and a point?
4. How does the gradient relate to parallel and perpendicular lines?
5. Can you find the gradient between two points if they are given as fractions?

**Tip:** Always choose clear points on the grid when calculating the gradient, preferably those where the line crosses exact coordinates (integer values).

Find out how to calculate the gradient of a line using coordinate geometry. This example uses points from the Cartesian plane to apply the gradient formula and derive the slope of the blue line. Suitable for students in Grades 7-9.

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