Different Forms Of 2D Linear Equations

Students will often have to solve for different components of linear functions, especially if they are being asked to graph them. Knowing the terminology and different forms can be very helpful.

General Form,

        Ax + By + C = 0

A and B are real numbers. If A is nonzero, then the x-interceptis −C/A. If B is nonzero, then the y-intercept is −C/B, and the slope of the line is −A/B.

Standard form

        Ax + By = C

Very similar to the standard form, the only difference being the constant C is on the opposite side of the equals sign.

Slope–intercept form

        y = mx + b

The most common form and often the most useful. M stands for the slope of the graph, the change in y over the change in x, also often referred to as rise over run, and b stands for the y-intercept. These are two of the most sought-out components of a graph, and it is often useful to convert into slope-intercept form before graphing.

Point-slope form

        (y - y₁) = m(x - x₁),

Where m is the slope of the line and (x₁,y₁) is any point on the line. The point-slope and slope-intercept forms are easily interchangeable. When given a point and the slope it is often useful to start out in point-slope form and then to convert into slope-intercept form.