Call Now: (800) 537-1660  
The Algebra Buster
The Algebra Buster
page description



December 22nd









December 22nd

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.

Example

Graph of a Line

Graph 3x + 2y = 12.

Algebra Buster software can easily solve any algebra problem including graphing lines such as this one. See how Algebra Buster solves a similar problem

Solution

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 x-intercept.

Example

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.

Solution

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 Example 14.

Example

Graph of a Line Through the Origin

Graph y = -3x.

Solution

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 and you will also receive 30 minutes of free live tutoring from tutor.com!

 

 
 

Copyright © 2007-2014, algebra-online.com. All rights reserved.



Related pages: