One of the biggest advantages of the general form of a linear equation is that it can be used to represent any linear relation, including vertical lines. The slope-intercept form cannot be used for vertical lines because the slope of a vertical line is not defined.

In the Investigation, you may have discovered that the equations of horizontal lines can be reduced to the form y = b, where b represents the y-intercept.

Notice that regardless of the x-value, the y-value always remains the same.

Since the value of x has no effect on the value of y, the equation of a horizontal line can be written using just y.

In the Investigation, you may also have discovered that the equations of vertical lines can be reduced to the form x = a, where a represents the x-intercept.

Notice that regardless of the y-value, the x-value always remains the same.

Since the value of y has no effect on the value of x, the equation of a vertical line can be written using just x.

Most lines have two intercepts: one x-intercept and one y-intercept. Vertical and horizontal lines are special because they do not have two intercepts. Most horizontal lines have only a y-intercept and most vertical lines have only an x-intercept. The x-axis and the y-axis represent lines that have more than two intercepts. You will explain why this is the case in Practice - II.