Objectives
After reviewing this unit, you will be able to:
Graphing an Equation
In section one we introduced an example using the cost of pizza
based on the number of toppings on the pizza. In this example,
a plain pizza with no toppings was priced at 7 dollars. As you
add one topping, the cost goes up by 75 cents. (If you wish to
review the example, return to the first
unit.) We found the equation that relates the total price
of a pizza to the number of toppings on the pizza to be y
= 7.00 + .75x. Now let's look at how you can draw a graph
that illustrates this relationship. The procedure for doing this
is:
Now let's work through these steps with our pizza example:
In the pizza example, the equation is y = 7.00 + .75x. You first select values ofx you will solve for. You then substitute these values into the equation and solve for they values. Your list of points may be kept in a table like the one below. For our pizza example, a table may start out this way:
x Number of Toppings 
y Final Cost 

0  7.00 
1  7.75 
2  
3  
4 
In the table below, for each givenx value you can see the calculation of each of they values.
x Number of Toppings 
y Final Cost 


Let x = 0: y = 7.00
+ .75 (0) y = 7.00 + 0 y = 7.00 
0  7.00 
Let x = 1: y = 7.00
+ .75 (1) y = 7.00 + .75 y = 7.75 
1  7.75 
Let x = 2: y = 7.00
+ .75 (2) y = 7.00 + 1.50 y = 8.50 
2  8.50 
Let x = 3: y = 7.00
+ .75 (3) y = 7.00 + 2.25 y = 9.25 
3  9.25 
Let x = 4: y = 7.00
+ .75 (4) y = 7.00 + 3.00 y = 10.00 
4  10.00 
After you have completed your table, you should end up with the following list of points:
Notice they are written using the (x, y) notation. You are now ready to create the graph of these points on a set of axes.
Once you have your list of points you are ready to plot them on a graph. The first step in drawing the graph is setting up the axes and determining the scale. The points you have to plot are: Notice that thexvalues range from 0 to 4 and theyvalues go from 7 to 10. The scale of the two axes must include all the points. Below is a set of axes drawn to do just that. Notice that the distance between the points must be equal on each axis but does not have to be the same for both axes. The xaxis goes up to 5 on this diagram, and the yaxis up to 10; the scale on each axis can be different. 
After you have drawn the axes, you are ready to plot the points. (How to plot points was discussed in the first part of this book. If you feel you need to review this, reread the discussion on plotting points in the second unit.) Below we plot the points on a set of axes. 
Once you have plotted each of the points, you can connect them and draw a straight line. 
Checking
a Point in the Equation
If, by chance, you have a point and you wish to determine if it
lies on the line, you simply go through the same process as generating
points. Use the x value given in the point and insert it
into the equation. Compare the y value calculated with the
one given in the point.
Example
Does point (6, 10) lie on the line y = 7.00 + .75 x given in our pizza example? To determine this, we need to plug the point (6, 10) into the equation.
x
Number of Toppingsy
Final CostLet x = 6
y = 7.00 + .75 (6)
y = 7.00 + 4.50
y = 11.506 11.50 As we can see here, the point with an x value of 6 that does lie on the line is (6, 11.5). This means that the point (6, 10) does not lie on our line.
You are now ready to try graphing an equation. Move on to the first practice for this unit. If you have already completed the first problem try the additional pratice before moving on.
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