https://file.aiquickdraw.com/mathbot/file/1733355330008ngk4m4vc.jpg

To find the gradient (slope) of the line passing through the points \((3,1)\) and \((8,36)\), we use the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the given points:

\[
m = \frac{36 - 1}{8 - 3} = \frac{35}{5} = 7
\]

### Final Answer:
The gradient of the line is \(7\).

Would you like further explanation or details? Here are some related questions to expand your understanding:

1. How do you calculate the equation of the line using the gradient and a point?
2. What does the gradient represent in a real-world context?
3. Can the gradient be negative, and what would that signify?
4. How would you verify the gradient using a graph?
5. What happens to the gradient if the two points are swapped?

**Tip:** Always simplify the fraction when calculating the gradient to ensure your answer is in its simplest form!

What is the gradient of the line passing through the points (3, 1) and (8, 36)? Give your answer as an integer or as a fraction in its simplest form.

Learn how to calculate the gradient of a straight line that passes through the points (3, 1) and (8, 36). This problem explores essential algebraic concepts and the gradient formula, suitable for students in Grades 7-9.

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