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To find the slope of line \( \overrightarrow{AB} \) given the points \( A(4, 5) \) and \( B(9, 7) \), we use the slope formula:

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

Where \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of points A and B, respectively.

Substitute the given points into the formula:

\[
\text{slope} = \frac{7 - 5}{9 - 4} = \frac{2}{5}
\]

Thus, the slope of line \( \overrightarrow{AB} \) is \( \frac{2}{5} \).

The correct answer is:

\[
\boxed{\frac{2}{5}}
\]

Would you like more details or have any questions?

Here are five related questions to explore:

1. How do you interpret the meaning of a positive slope in a real-world context?
2. Can the slope formula be applied to vertical lines? Why or why not?
3. How would the slope change if one of the points were moved horizontally or vertically?
4. What is the equation of the line \( AB \) in slope-intercept form?
5. How can you find the midpoint of line segment \( AB \)?

**Tip:** When finding the slope, always pay attention to the order of the coordinates, as reversing them will give the negative of the correct answer!

Line AB contains points A(4, 5) and B(9, 7). What is the slope of AB?

Learn how to calculate the slope of line AB given points A(4,5) and B(9,7) with a detailed step-by-step solution. This problem covers algebraic concepts and the slope formula, ideal for students in Grades 7-10.

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