Graphing Using x- and y- Intercepts
Once we know both the x-intercept and the y-intercept, we can
graph the equation.
Graph 3x + 5y = 15 using the x- and y- intercept.
First, find the intercepts.
|To find the y -intercept, let
x = 0.
||To find the x-intercept, let
y = 0.
|3 Â· 0 + 5y
||3x + 5 Â· 0
|The y-intercept is 3.
||The x-intercept is 5.
|The ordered pair is (0, 3).
||The ordered pair is ( 5, 0)
We now graph these two points and draw the line that contains
The slope-intercept form is a special case of the point-slope
form, where the given point of the line (x 0 , y
0 ) lies on the y-axis, so x 0 = 0. This means
that the equation is of the form y - y 0 = mx, or y =
mx + y 0 . So, the equation is given explicitly when
we know both the intercept and the slope and it is simpler than
the more general point-slope form. This is the most common form
for the equation of a line.
Key Idea An equation for a line is said to be
in slope-intercept form when it is of the form y = mx + b, where
m is the slope of the line and b is the y-coordinate of the
y-intercept. Any line that is not vertical has an equation that
can be written in slope-intercept form.
The equation of a vertical line cannot be written in
slope-intercept form because the slope of a vertical line is
undefined; that is, it has no slope.