Determine the slope of the line through the given points (3,5) and (5,10)

The slope of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:

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

For the points \((3, 5)\) and \((5, 10)\), we substitute into the formula:

\[
\text{slope} = \frac{10 - 5}{5 - 3} = \frac{5}{2}
\]

Thus, the slope of the line is:

\[
\text{slope} = \frac{5}{2}
\]

Would you like further details or have any questions?

Here are 5 related questions for practice:
1. What is the equation of the line passing through the points (3, 5) and (5, 10)?
2. How do you determine if two lines are parallel based on their slopes?
3. If a line has a slope of \(\frac{5}{2}\), what is the slope of a line perpendicular to it?
4. How do you find the y-intercept of a line given its slope and one point?
5. Can you find the distance between the points (3, 5) and (5, 10)?

**Tip:** The slope of a horizontal line is always zero, and the slope of a vertical line is undefined.

Learn how to calculate the slope of a line passing through the points (3, 5) and (5, 10) using the slope formula. This example helps students understand key algebraic concepts and coordinate geometry, suitable for Grades 6-8.

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