Flashcard Review-Slope and Equation of a Line

The slope of a line is a measure of its steepness, usually represented as 'm' in the equation of a line. It is calculated as the change in y divided by the change in x (rise over run).

The y-intercept is the point where the line crosses the y-axis. It can be found by setting x to 0 in the equation of the line.

The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

The slope (m) is calculated as (7 - 3) / (4 - 2) = 4 / 2 = 2.

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

The slope of a vertical line is undefined because the change in x is zero, leading to division by zero.

The slope of a horizontal line is 0 because there is no change in y as x changes.

A slope of 3 means that for every 1 unit increase in x, y increases by 3 units.

To determine the slope from a graph, select two points on the line, calculate the rise (change in y) and run (change in x), and then divide rise by run.