EDGE Math 8

Forms of Linear Equations

Slope-Intercept Form

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

y = m x + b,

where m is the slope and b is the y-intercept of the line.

The slope-intercept form can be derived this way. Suppose it is given that the slope of a line is m and the y-intercept of the line is b. Note that you can identify a point of the line using the y-intercept b. Such point is $(0, b) .$ Since you now have the slope and a point, you can write the equation of the line in point-slope form, where $(x_{1}, y_{1}) = (0, b) .$

\begin{array}{l} y - y_{1} = m (x - x_{1}) \\ y - b = m (x - 0) \\ y - b = m x \\ y = m x + b \end{array}

Notice that the last equation is already the slope-intercept form of the equation of a line.