Equations that Meet on a Graph

Date: 03/09/2002 at 19:38:13
From: Karyn 
Subject: Slopes

How am I supposed to graph d = 30t and d = 28t+12? I don't understand 
how to graph them. d is distance and t is time. The two equations are 
supposed to meet on the graph. I tried the question by starting on the 
origin and then going to 30 for the first equation and for the second 
equation I went over 12 and then went up 28. The two equations didn't 
meet. I need help with them meeting on the graph and how they are 
supposed to be graphed.

Date: 03/09/2002 at 20:25:20
From: Doctor Jeremiah
Subject: Re: Slopes

Hi Karyn:

d is called the dependant variable, because it depends on whatever 
value of t you put in. The dependant variable is always the vertical 
height on the graph. Most of the time the height is a variable called 
y but it doesn't have to be; in this case it's d.

t is called the independant variable, because it does not depend on 
anything; you just put in values for t. The independant variable is 
always the distance across horizontally on the graph. Most of the time 
the height is a variable called x but it doesn't have to be; in this 
case it's t.

So to plot a point on the graph you decide on a value for t and figure 
out what the corresponding value of d is equal to. You should do this 
for as many values of t as possible. Then you connect the dots.

When you have two equations, do them separately, one after the other.  
That way when you connect the dots you won't get confused.

So, for example, using d = 30t you would pick values for t and get 
corresponding values for d that you can plot:

   across (t)       height (d)
--------------------------------
     -3                -90
     -2                -60
     -1                -30
      0                  0
      1                 30
      2                 60
      3                 90

And when you plot the these points, it looks like this:

                             |
                         90 -|-                X (3,90)
                             |
                             |
                         60 -|-          X (2,60)
                             |
                             |
                         30 -|-    X (1,30)
                             |
           3     2     1     |
      -----|-----|-----|-----X-----|-----|-----|-----
                             |     1     2     3
                             |
              (-1,-30) X    -|- -30
                             |
                             |
        (-2,-60) X          -|- -60
                             |
                             |
  (-3,-90) X                -|- -90
                             |

Now you connect these points and then you can do the second equation 
and connect those points. Then you can find the intersection.

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