C. x- and y-Values for Horizontal and Vertical Lines
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.