Graph Linear Functions

A linear function is a function that creates 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 the y-value with respect to the x-value. It shows how steep the line is.

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

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

The equation of a horizontal line is y = b, where b is the y-value for all points on the line.

The equation of a vertical line is x = a, where a is the x-value for all points on the line.

Two lines are parallel if they have the same slope and will never intersect.

Two lines are perpendicular if the product of their slopes is -1. This means they intersect at a right angle.

To determine if a point (x, y) lies on a line represented by an equation, substitute the x-value into the equation and see if the resulting y-value matches.

The average rate of change between two points on a line is the change in y divided by the change in x, often interpreted as the slope.