Graphing Linear Equations

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

A slope is positive if the line rises from left to right and negative if it falls from left to right.

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

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

The Slope-Intercept Form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

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

To graph a linear equation in slope-intercept form, start at the y-intercept (b) on the y-axis, then use the slope (m) to determine the rise over run to find another point.

In real-world applications, the slope can represent rates such as speed, cost per item, or any other rate of change.

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y to isolate it on one side of the equation.