Question

how to find the slope of a line given two points

Answer 1

To find the slope of a line given two points, you can use the slope formula. The slope (\(m\)) is calculated using the coordinates of the two points. Let's say the two points are \((x_1, y_1)\) and \((x_2, y_2)\). The formula for the slope is:

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

Here are the steps to follow:

1. Identify the coordinates of the two points. For example, let’s say the points are \(A(2, 3)\) and \(B(5, 11)\). In this case, \(x_1 = 2\), \(y_1 = 3\), \(x_2 = 5\), and \(y_2 = 11\).

2. Substitute these values into the slope formula:

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

3. Simplify the calculations:

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

So, the slope of the line that passes through the points \(A(2, 3)\) and \(B(5, 11)\) is \(\frac{8}{3}\).

Remember:
- If \(x_2 - x_1 = 0\), the slope is undefined (the line is vertical).
- If \(y_2 - y_1 = 0\), the slope is 0 (the line is horizontal).