Slope of a Straight Line
What is Slope?
The slope of a straight line is a number that describes both the steepness and the direction of the line. It tells us how much the line rises or falls as we move from left to right.
Formal Definition: The slope of a line passing through two distinct points $(x_1, y_1)$ and $(x_2, y_2)$ is defined as the ratio of the change in $y$ to the change in $x$: $$ m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} $$where $x_2 \neq x_1$.
We often describe slope as: $$ m = \frac{\text{rise}}{\text{run}} $$
Types of Slope
Positive Slope
↗
$m > 0$
Line rises from left to right
Negative Slope
↘
$m < 0$
Line falls from left to right
Zero Slope
→
$m = 0$
Horizontal line
Undefined Slope
↑
$m = $ undefined
Vertical line