Linear Functions Check

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 y with respect to x. It indicates how steep the line is and the direction it goes (positive slope means the line rises, negative slope means it falls).

To find the y-intercept of a linear equation in the form y = mx + b, set x = 0 and solve for y. The y-intercept is the point where the line crosses the y-axis.

The x-intercept is the point where the line crosses the x-axis. To find it, set y = 0 in the equation and solve for x.

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 convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y in terms of x.

The slope (m) between two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1).

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 line has a slope that is the negative reciprocal of the other.

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