Plotting Coordinates on a Graph

Date: 07/02/99 at 20:55:09
From: craig  hill
Subject: Positive and negative numbers on a graph

The graph I am looking at has a Y at the top of the vertical line and 
an X on the horizontal line. Zero intersects the two lines in the 
middle. 

Y from top to bottom is: 5 4 3 2 1 0 1 2 3 4 5. 
X' from side to side is: -5 -4 -3 -2 -1 0 1 2 3 4 5. 

The instructions say that horizontal line numbers to the right are 
positive numbers. Numbers to the left of zero are negative numbers. On 
the vertical Y axis, the numbers above the zero are positive, and the 
numbers below are negative numbers. Then there are some questions at 
the end of the chapter:

     3+(-2) =     (-4)+(-1) =     (-2)+5 =     (-5)+5 =

It then says to locate these order pairs on the coordinate graph (it 
shows the graph in a grid):

     (-4,3) mark as A     (-2,-3) mark as B     (4,4) mark as C
     (3,-2) mark as D

I am already having a lot of trouble in school with math and need to 
get it right before school starts in fall.

Thank you.
C.B.

Date: 07/03/99 at 12:23:28
From: Doctor Peterson
Subject: Re: Positive and negative numbers on a graph

Hi, Craig.

The first set of questions is about positive and negative numbers on 
the number line:

      +---+---+---+---+---+---+---+---+---+---+
     -5  -4  -3  -2  -1   0   1   2   3   4   5

To add two numbers, just picture standing at the zero and facing to 
the right. A positive number tells you to walk forward that many 
steps, and a negative number means to walk backwards. For example, 
3 + -2 means walk forward 3 steps (to the 3), then backward 2 steps. 
The first step takes you to 2, and the second takes you to 1, so 
that's the answer. What you're really doing is just undoing 2 of the 
3 steps you took to the right or subtracting 2 from 3. If you go back 
more than 3 steps, you will pass zero and go negative; the distance 
you would end up from zero would be the difference between the two 
distances you walked. For example, 3 + -5 is -2, because the first 
3 steps backward take you to 0, and you have 5 - 3 = 2 more steps to 
take.

See how well you can work out the rest of those problems thinking this 
way.

The other set of problems relates to this graph, where we use pairs 
of numbers to identify points, just as we use one number to name 
points on the number line:

                          Y
                         5+
                          |
                         4+
                          |
                         3+
                          |
                         2+
                          |
                         1+
                          |
      +---+---+---+---+---+---+---+---+---+---+ X
     -5  -4  -3  -2  -1   |   1   2   3   4   5
                        -1+
                          |
                        -2+
                          |
                        -3+
                          |
                        -4+
                          |
                        -5+

Point A is (-4, 3), which means you want X to be -4 and Y to be 3. X 
is the distance left or right from the vertical line, so we can draw a 
line vertically through "-4" on the X axis, marking all the points 
that are 4 units left of the Y axis:

                          Y
          |              5+
          |               |
          |              4+
          |               |
          |              3+
          |               |
          |              2+
          |               |
          |              1+
          |               |
      +---+---+---+---+---+---+---+---+---+---+ X
     -5  -4  -3  -2  -1   |   1   2   3   4   5
          |             -1+
          |               |
          |             -2+
          |               |
          |             -3+
          |               |
          |             -4+
          |               |
          |             -5+

Y is the distance up or down from the horizontal line, so we can draw 
another line through 3 on the Y axis:

                          Y
          |              5+
          |               |
          |       4      4+
          |A     left     |
      ----+--------------3+--------------------
          |               |
          |              2+
          |3 up           |
          |              1+
          |               |
      +---+---+---+---+---+---+---+---+---+---+ X
     -5  -4  -3  -2  -1   |   1   2   3   4   5
          |             -1+
          |               |
          |             -2+
          |               |
          |             -3+
          |               |
          |             -4+
          |               |
          |             -5+

The place where these two lines intersect is A, because it's 4 units 
to the left and 3 units up. The coordinates (-4, 3) mean "walk 4 steps 
to the left, then 3 steps up".

Try finding the rest of the points the same way. If you need more 
help, feel free to write back. That's what we're here for!

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