Graph of a Line
We can graph the linear equation defined by y = x + 1 by
finding several ordered pairs. For example, if x = 2 then y = 2 +
1 = 3, giving the ordered pair (2, 3). Also, (0, 1), (4, 5), (-2,
-1), (-5, -4), (-3, -2), among many others, are ordered pairs
that satisfy the equation.
Get a PDF of similar solved problems sent to you!
To graph y = x + 1 we begin by locating the ordered pairs
obtained above, as shown in Figure 6(a). All the points of this
graph appear to lie on a straight line, as in Figure 6(b). This
straight line is the graph of y = x + 1.
It can be shown that every equation of the form ax + by = c
has a straight line as its graph. Although just two points are
needed to determine a line, it is a good idea to plot a third
point as a check. It is often convenient to use the x- and
y-intercepts as the two points, as in the following example.
Graph of a Line
Graph 3x + 2y = 12.
Algebra Buster software can easily solve any algebra problem
graphing lines such as this one.
See how Algebra Buster solves a similar problem
To find the y -intercept, let x = 0.
|3(0) + 2y = 12
|2y = 12
||Divide both sides by 2.
|y = 6
Similarly, find the x-intercept by letting y = 0 which gives x
= 4. Verify that when x = 2 the result is y = 3. These three
points are plotted in Figure 7(a). A line is drawn through them
in Figure 7(b).
Not every line has two distinct intercepts; the graph in the
next example does not cross the x-axis, and so it has no
Graph of a Horizontal Line
Graph y = -3.
Algebra Buster software will show you all the steps and explanations
if you need them. Here are
some examples. Our software actually helps you
learn Algebra so there is no need to hire an expensive tutor.
The equation y = -3 or equivalently y = 0x -3, always gives
the same y -value, - 3, for any value of x . Therefore, no value
of x will make y = 0, so the graph has no x -intercept. The graph
of such an equation is a horizontal line parallel to the x -axis.
In this case the y -intercept is - 3, as shown in Figure 8.
In general, the graph of y = k, where k is a real number, is
the horizontal line having y-intercept k.
The graph in Example 13 had only one intercept. Another type
of linear equation with coinciding intercepts is graphed in
Graph of a Line Through the Origin
Graph y = -3x.
Begin by looking for the x -intercept. If y = 0 then
|y = -3x
|0 = -3x
||Let y = 0
|0 = x
||Divide both sides by -3
We have the ordered pair (0, 0). Starting with x = 0 gives
exactly the same ordered pair, (0, 0). Two points are needed to
determine a straight line, and the intercepts have led to only
one point. To get a second point, choose some other value of x
(or y ). For example, if x = 2 then
y = -3x = -3(2) = -6, (let x = 2)
giving the ordered pair (2, -6). These two ordered pairs, (0,
0) and (2, -6), were used to get the graph shown in Figure 9.
Buy and download Algebra Buster now
you will also receive 30 minutes of free live tutoring from tutor.com!