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Part 1
Select the answer that best completes the given statement.
Question content area bottom
Part 1
The​ slope, m, of a line through the distinct points left parenthesis x 1 comma y 1 right parenthesis and left parenthesis x 2 comma y 2 right parenthesis is given by the formula mequals
▼ 
StartFraction x 2 minus x 1 Over y 1 minus y 2 EndFraction .
StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction .
StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction .
StartFraction y 2 minus y 1 Over x 1 minus x 2 EndFraction .

The formula for the slope \( m \) of a line passing through two distinct points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:

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

This formula represents the change in the \( y \)-coordinates divided by the change in the \( x \)-coordinates (also called "rise over run").

Therefore, the correct answer is:

\[
\boxed{\frac{y_2 - y_1}{x_2 - x_1}}
\]

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. How do you find the slope of a line if given points \( (3, 7) \) and \( (5, 11) \)?
2. What does a slope of zero mean for a line?
3. How do you interpret a negative slope?
4. What happens if \( x_2 = x_1 \) when calculating the slope?
5. How does the slope formula change in three dimensions?

**Tip**: The slope is positive when the line rises from left to right, and negative when it falls from left to right.

The slope, m, of a line through the distinct points (x₁, y₁) and (x₂, y₂) is given by the formula: StartFraction y₂ - y₁ Over x₂ - x₁ EndFraction.

Understand how to calculate the slope of a line through two points using the slope formula (m = (y₂ - y₁) / (x₂ - x₁)). This concept is essential in coordinate geometry and linear equations. Suitable for students in Grades 8-10.

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