Question 817813
   The equation is already given here , but if it wasn't how would you
  arrive at the equation ?
  Notice the rate of change :  80 meters per minute
   The change is constant .  80 meters EVERY minute.
  A constant rate of change indicates a linear equation which 
  can always be written as:
    Output variable = rate of change(input variable)  + starting value of output
How do you determine what the output and input variables are?
   Look at the rate of change :  80 meters per minute .
   There is one number and 2 words .
   The FIRST word, meters, represents the OUTPUT variable .
    Let's not use m, but ask what quantity is being measures in meters.
 The DEPTH is being measured in meters, so we will use the variable 
   d to represent the output depth.
  The SECOND word , minute, refers to the input variable 
 so use the variable m to represent the # of minutes.
The equation comes from this sentence:
  To find depth of sub, multiply # of minutes times 80 and add it to the starting value -7500.
        d = 80m + -7500
        Table


           m.                  d
         # of min.         depth, in meters 
        values of.           values of
         DOMAIN.          RANGE 
            0.                  -7500
         10.                   -6700
          50.                   -3500
         90.                    -300
           .?                        0.     This is the highest value of sub, sea level , 0 elevation!!!
       100.                    500.      THIS cannot happen.   The depth of the sub cannot be > 0!!!

         The range has values from -7500 meters (starts 7500 BELOW sea level)  to 0 meters.
      The domain (possible values for input) starts at 0 minutes, but these # of minutes will
      Stop when the sub has reached sea level  when output or depth  = 0.
     How many minutes does it take for sub to surface , when d, depth = 0?
      Go back to equation  :   d = 80 m + -7500
                   Replace d with 0
          0 = 80m + -7500
       solve for m to get m = 93.75 minutes 
    So the domain, possible values for # of minutes in which the sub rises goes from 
       0 to 93.75
    When you graph this the  y or vertical intercept, where graph crosses vertical  axis,
     has 0 for the  x value, input value 
      so the point is (0, -7500).  or.  (0 min,  -7500 meters)

  The  x or horizontal intercept , where graph crosses horizontal axis,
     has 0 for the  y or output value.  (93.75. min,  0 meters )
 Remember.   y- intercept ?      x = 0.   (0,?)
     x-intercept ?    y = 0.       ( ?, 0)