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 y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

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 point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

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

The x-intercept is the point where the graph crosses the x-axis (y=0), and the y-intercept is where it crosses the y-axis (x=0).

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

A proportional relationship is one where the ratio of y to x is constant, which means the graph of the relationship is a straight line that passes through the origin.

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

The y-intercept indicates the value of y when x is zero, representing the starting point of the line on the y-axis.