Question

How to calculate the slope of a line given two points

Answer 1

To calculate the slope of a line given two points, you can use the slope formula:

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

Where:
- \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of the two points.

Here are the steps:

1. Identify the coordinates of the two points. For example, let's say you have points \( A(x_1, y_1) = (2, 3) \) and \( B(x_2, y_2) = (5, 11) \).
2. Plug the values into the formula:
- \( x_1 = 2 \), \( y_1 = 3 \)
- \( x_2 = 5 \), \( y_2 = 11 \)

3. Substitute into the formula:

\[
m = \frac{11 - 3}{5 - 2}
\]

4. Simplify the calculation:

\[
m = \frac{8}{3}
\]

So, the slope of the line connecting the two points (2, 3) and (5, 11) is \( \frac{8}{3} \).

Remember that:
- A positive slope indicates that the line rises from left to right.
- A negative slope indicates that the line falls from left to right.
- A slope of zero indicates a horizontal line, while an undefined slope (when \( x_1 = x_2 \)) indicates a vertical line.