Graphing and Intercepts
- The selection of points to use when graphing a linear
equation in two variables need not be random. Two points
which are (generally) easy to get and also useful in
applications are the horizontal and vertical intercepts.
These both exist provided that the line in question is
not horizontal or vertical.
The horizonal (or x-) intercept of a line (if
it exists) is the point where the line crosses the horizontal
The vertical (or y-) intercept of a line (if
it exists) is the point where the line crosses the vertical axis.
Procedure: (Finding Intercepts)
To find the horizontal intercept, set the vertical variable to
0 and solve for the horizontal variable. (Most of the time, this
means that you set y = 0 and solve for x .)
To find the vertical intercept, set the horizontal variable to
0 and solve for the vertical variable. (Most of the time, this
means that you set x = 0 and solve for y .)
- There are two types of lines for which this does not
work: horizontal lines and vertical
lines . Luckily, horizonal and vertical lines
are very easy to spot when given an equation.
Assuming that the horizontal variable is x and the vertical
variable is y , then any vertical line has an equation of the
form x = a and any horizontal line has an equation of the form y
= b .