Linear Functions REVIEW

A linear function is a function that can be graphically represented as a straight line. It has 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 function. It indicates how much y changes for a unit change in x.

To find the slope from a table, select two points (x1, y1) and (x2, y2) and use the formula: slope (m) = (y2 - y1) / (x2 - x1).

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.

Compare the coefficients of x (the slopes) in the equations. The function with the larger coefficient has the greater slope.

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

To graph a linear function, identify the y-intercept, plot it on the graph, and use the slope to find another point. Draw a straight line through the points.

Two lines are parallel if they have the same slope but different y-intercepts. They will never intersect.

Two lines are perpendicular if the product of their slopes is -1. This means one slope is the negative reciprocal of the other.

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