Old Ch. 3 - Slope/Slope-intercept Form

Slope is a measure of the steepness of a line, represented as the ratio of the vertical change to the horizontal change between two points on the line.

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

A slope is undefined when the line is vertical, meaning there is no horizontal change (the denominator of the slope formula is zero).

A slope of zero indicates that the line is horizontal, meaning there is no vertical change as you move along the line.

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

The y-intercept (b) is the point where the line crosses the y-axis, represented by the value of y when x = 0.

A slope of 4 means that for every 1 unit you move horizontally (run), the line rises 4 units vertically (rise).

The equation of the line is y = -5/3x + 1.

To convert from slope-intercept form (y = mx + b) to standard form (Ax + By = C), rearrange the equation to get all terms involving x and y on one side.

The slope can represent rates of change, such as speed, cost per item, or any other relationship where one quantity changes in relation to another.