T-Charts and Graphs

Date: 11/11/2001 at 21:29:56
From: Dr.Anjo
Subject: T-charts and graphs

Hello Dr.Math,
I'm having trouble understanding this problem: 

Make a table of values for the line y = x/4+4 using x-values of 
1,2,3,4, and 5. Which graph shows the line that passes through the 
ordered pairs of the table?

I can't show the graphs but I need to know the steps. My teacher told 
me to make an x/y chart. If I remember correctly, you have to do 
something along the lines of dividing 4 into x and then ? 

Thanks,
Dr. Anjo (I want to be a children's doctor)

Date: 11/12/2001 at 13:12:55
From: Doctor Peterson
Subject: Re: T-charts and graphs

Hi, Doctor!

First, you have to have a clear idea what y = x/4 + 4 means. This is 
an equation that tells you that, for any value of x, you can find y by 
dividing by 4 and then adding 4. Does that sound familiar? Your 
teacher was just telling you to read the equation and do what it says.

Now, what is the table you have to make? You will list several values 
of x (which you will be using as x-coordinates in your graph), and for 
each one use the equation to find what y is. I'll show the work:

    For x = 1, y = 1/4 + 4 = 4.25

    For x = 2, y = 2/4 + 4 = 4.5

    For x = 3, y = 3/4 + 4 = 4.75

    For x = 4, y = 4/4 + 4 = 5

    For x = 5, y = 5/4 + 4 = 5.25

Do you see what I did there? I just replaced x in the equation by each 
value of x, and did the division and addition.

Now your table will look like this:

    x |  y
    --+-----
    1 | 4.25
    2 | 4.5
    3 | 4.75
    4 | 5
    5 | 5.25

Each of these pairs gives you a point on the graph. Now you can draw 
the graph; or, in this problem, just look at the given graphs to see 
whether they include the five points you've found. It will look like 
this:

     |
     |
     |              o
    5+           o  (5,5.25)
     |        o  (4,5)
     |     o  (3,4.75)
     |  o  (2,4.5)
    4+  (1,4.25)
     |
    ...
     +--+--+--+--+--+->
     0  1  2  3  4  5

Let me know if you need any more help with this. You may also want to 
browse the Dr. Math archives:

   Graphing Equations
   http://mathforum.org/dr.math/tocs/graph.eq.middle.html   

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/