EDGE Math 8

Forms of Linear Equations

General Form

The following is the general form of the equation of a line:

A x + B y + C = 0,

where A, B, and C are real numbers and where both A and B are not equal to 0.

Point-Slope Form

The following is the point-slope form of the equation of a line:

y - y_{1} = m (x - x_{1}),

where $(x_{1}, y_{1})$ is a point on the line and m is the slope of the line.

The point-slope form of the equation of the line can be derived from the formula for the slope. Suppose $P (x_{1}, y_{1})$ is a given point of the line, $Q (x, y)$ is any point on the line, and m is the slope of the line. You have learned that:

\frac{y - y_{1}}{x - x_{1}} = m .

Multiplying both sides of the equation above by $x - x_{1},$ you will have:

y - y_{1} = m (x - x_{1}) .

Notice that this equation is the point-slope form that was previously presented.