A Scuba diver starts a dive with a full tank of oxygen. While diving, She breathes at a constant rate. She checks the gauge after 22 minutes. What does a graph of the function look like ?

The correct answer is: (- a)/44 x + a

SOL – It is given that the scuba driver breathes at a constant rate.
 Rate of change = Slope of the graph = k (constant)
 Graph is a straight line because a straight – line graph has constant slope.
Note – We can also find linear function of the graph.
Let amount of oxygen in the tank = y
Time taken = x minutes
In the figure, when time, x = 0 oxygen tank is full.
Let the amount of oxygen when tank is full be a
i.e., x = 0, y = a
In the figure, after 22 min, amount of oxygen is reduced to half.
i.e.  x = 22, y =
Using two – point form, equation of the line is
(y – y₁) = m (x – x₁) where m = 
Slope = 
=.   =  =
Equation of line is (y – a) =(x – 0)
 y – a = x
 y =  x + a