https://file.aiquickdraw.com/mathbot/file/1727196264607ri3kznho.jpg

The image shows two points, \( P_1(2, 5) \) and \( P_2(5, 14) \). To find the slope of the line passing through these two points, we use the slope formula:

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

Here, \((x_1, y_1) = (2, 5)\) and \((x_2, y_2) = (5, 14)\). Substituting these values into the formula:

\[
m = \frac{14 - 5}{5 - 2} = \frac{9}{3} = 3
\]

So, the slope of the line is \( m = 3 \).

Would you like any further explanation or details?

Here are 5 related questions to expand your understanding:
1. What is the equation of the line passing through the points \( P_1(2, 5) \) and \( P_2(5, 14) \)?
2. How would you find the slope of a line parallel to this one?
3. What would the slope of a line perpendicular to this one be?
4. Can you verify the slope using a different pair of points on the line?
5. How does the slope change if you switch the order of the points?

**Tip:** When calculating the slope, make sure you are consistent with the order of subtraction for the coordinates; always subtract in the same order for both the \(x\) and \(y\) values.

Learn how to calculate the slope of a line passing through the points (2, 5) and (5, 14) using the slope formula. This problem demonstrates key algebraic concepts and is suitable for students in Grades 7-9.

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