Think through 67 (section 3.2) something like this:  If I bought 4 dinners and 10 lunches, how would I figure out the total?

 

 

If I bought 8 dinners and 20 lunches, I would have:

 

 

So let’s write this using by arbitrary d and l

 

 

That is our equation.  Now we need to solve for one of the variables and graph it.  I will solve for l –it won’t give me fractions.

 

 

When graphing this it does not matter which one is the “x” or which one is the “y”.  Typically, I let the one I solved for be on the vertical axis…but it does not really matter.

 

 

To plot points you may use the TI-83’s graphing or table feature.

Step 1.  Hit the Y= key

Step 2.  Let’s use the table feature.  Hit TBLSET (2nd WINDOW).  You need to change your Indpnt to Ask.  Don’t worry about the TbleStart or Tbl.  Also….leave the Depend to Auto. 

Changing the Indpnt to Ask will allow us to put in any points.  If we left it on Auto, it would automatically generate points ( in this case that start at –3 and increment by 1.

Step 3.  Once you do this, hit the TABLE key (2nd Graph).You should get the screen on the left.  If there are a few values in for X and Y1, just hit the DEL key until they are all gone.

Step 4.  Now we are ready to choose some values for x (which in our case is d…the number of dinners.  Certainly we cannot choose negative number of dinners.  Nor could we choose fractional (or decimal) numbers.  I chose 2, 4, and 6.  So if we bought 2 dinners we had to have bought 35 lunches if our total was 225. 

Step 5.  To graph this, we must first adjust the window. 

Hit the WINDOW key.  Obviously we don’t need to have negative values for Xmin or Ymin…let’s make them 0.  For now let’s try 10 for the Xmax (we may need to adjust this to 15…I want to be able to see it intersect the x-axis).  Looking at our table in the previous step, The maximum value for Y appears to be 45.  I usually make the Ymax a little larger…say 50.  I changed the Yscl to 5 just to make the axis look a little better.  Try it with 1 and you will see what I mean.

Step 6.  Now hit the GRAPH key.

 

You should get the graph on the left. 

 

 

 

On graph paper it may look like this

 

I have plotted the points on the graph that correspond with the points from the table (see step 4).

 

So these are some possible meal combinations for $225.

 

0 dinners

45 lunches

2 dinners

35 lunches

4 dinners

25 lunches

6 dinners

15 lunches

 

I hope this helps.