Slope From Two Ordered Pairs

Slope from Two Ordered Pairs

The slope tells you how steep a line is. When you know two points, use their coordinates to compare the change in y with the change in x.

1) Write the formula

For points ((x_1, y_1)) and ((x_2, y_2)), the slope is [ m = \frac{y_2 - y_1}{x_2 - x_1} ] This is often called “rise over run.”

2) Substitute carefully

Pick one point as the first point and the other as the second point. Keep the x-values together and the y-values together. A common mistake is mixing the coordinates or switching only one part of the subtraction.

3) Simplify the fraction

After subtracting, reduce the fraction if possible. If the numerator and denominator are both negative, the slope may become positive after simplification.

4) Check your work

You can check by using the points in both orders. The result should be the same. If you subtract in the opposite order for both numerator and denominator, the signs cancel and the slope does not change.

Useful reminders

• A positive slope goes up from left to right.
• A negative slope goes down from left to right.
• A slope of 0 means a horizontal line.
• If the denominator is 0, the slope is undefined.

Always give the final answer in simplest form.