find the gradient of the line that passes through the points (5,12) and (8,3)

To find the gradient (or slope) of the line that passes through the points \((5, 12)\) and \((8, 3)\), you can use the formula:

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

Here, \((x_1, y_1) = (5, 12)\) and \((x_2, y_2) = (8, 3)\).

Substituting these values into the formula:

\[
\text{Gradient} = \frac{3 - 12}{8 - 5} = \frac{-9}{3} = -3
\]

So, the gradient of the line is \(-3\).

Would you like more details on this, or do you have any questions?

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Here are 5 related questions:
1. How do you find the equation of the line with this gradient?
2. What does the negative gradient tell you about the line's direction?
3. How would the gradient change if the points were reversed?
4. What are the intercepts of the line with this gradient?
5. How does this gradient compare to a horizontal line's gradient?

**Tip:** Remember, a negative gradient indicates that the line is sloping downwards from left to right.

Learn how to find the gradient (or slope) of a line passing through the points (5, 12) and (8, 3) using the gradient formula. Understand the mathematical method to calculate the slope between two points in a Cartesian plane. Suitable for Grades 7-9 students and anyone interested in analytical geometry.

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