How to Calculate Slope
The slope represents the "steepness" of a line, often denoted as the "rise over run".
Slope Formula (Rise over Run)
$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$
"Rise" is the vertical change ($\Delta y$), and "Run" is the horizontal change ($\Delta x$).
Example Problem
Question: Find the slope of the line passing through A(1, 2) and B(4, 8).
Step 1: Find the rise (change in y).
$y_2 - y_1 = 8 - 2 = 6$
Step 2: Find the run (change in x).
$x_2 - x_1 = 4 - 1 = 3$
Step 3: Divide Rise by Run.
$m = 6 / 3 = 2$
Answer: The slope m = 2.
Types of Slope
- Positive Slope
(m > 0):
Line goes UP from left to right. - Negative Slope
(m < 0):
Line goes DOWN from left to right. - Zero Slope (m =
0):
Horizontal line (y is constant). - Undefined
Slope:
Vertical line (division by zero).
Frequently Asked Questions
What if the denominator is zero?
If $x_2 - x_1 = 0$, the line is vertical. In math, division by zero is undefined, so the slope is undefined.
What does a slope of 1 mean?
A slope of 1 means for every 1 unit you move right, you move 1 unit up. This creates a 45-degree angle.