Slope, Intercepts, and Graphing Lines

The slope of a line is a measure of its steepness, represented as the ratio of the rise (change in y) to the run (change in x). It is often denoted as 'm' in the equation of a line, y = mx + b.

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of 'b' in the equation y = mx + b.

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

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

The x-intercept is the point where the line crosses the x-axis, which occurs when y = 0.

To find the x-intercept, set y = 0 and solve for x: 9x = 36, so x = 4.

A positive slope indicates that the line rises from left to right, while a negative slope indicates that the line falls from left to right.

A slope of zero indicates a horizontal line, which means there is no change in y as x changes.

An undefined slope indicates a vertical line, where x remains constant while y changes.

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 use the formula m = rise/run.