Slope Cheat Sheet

Slope Definition

Slope is a measure of the steepness of a line. It represents the change in 'y' for every unit change in 'x'.

Example: A slope of 2 means that for every 1 unit increase in x, y increases by 2 units.

Positive Slope

A line that rises from left to right has a positive slope.

Example: Imagine walking uphill.

Negative Slope

A line that falls from left to right has a negative slope.

Example: Imagine walking downhill.

Zero Slope

A horizontal line has a slope of zero.

Example: y = 5 is a horizontal line with a slope of 0.

Undefined Slope

A vertical line has an undefined slope.

Example: x = 3 is a vertical line with an undefined slope.

Slope Formula

The slope (m) between two points (x1, y1) and (x2, y2) is calculated as: m = (y2 - y1) / (x2 - x1)

Example: Points (1, 2) and (4, 8): m = (8 - 2) / (4 - 1) = 6 / 3 = 2

Rise Over Run

Slope can also be understood as 'rise over run', where 'rise' is the vertical change (change in y) and 'run' is the horizontal change (change in x).

Example: If a line rises 3 units for every 1 unit it runs, the slope is 3/1 = 3.

Slope-Intercept Form

In the equation y = mx + b, 'm' represents the slope of the line, and 'b' represents the y-intercept.

Example: In the equation y = 3x + 2, the slope is 3 and the y-intercept is 2.

Finding Slope from a Graph

Choose two points on the line. Count the rise (vertical change) and the run (horizontal change) between the points. Divide the rise by the run to find the slope.

Example: If the line rises 4 units and runs 2 units, the slope is 4/2 = 2.

Parallel Lines

Parallel lines have the same slope.

Example: y = 2x + 3 and y = 2x - 1 are parallel because they both have a slope of 2.

Perpendicular Lines

Perpendicular lines have slopes that are negative reciprocals of each other. If one line has a slope of 'm', the perpendicular line has a slope of '-1/m'.

Example: If a line has a slope of 2, a perpendicular line has a slope of -1/2.