Marion is observing the velocity of a cyclist at different times. after two hours, the velocity of the cyclist is 18 km/h. after four hours, the velocity of the cyclist is 4 km/h. part a: write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. show your work and define the variables used. (5 points) part b: how can you graph the equations obtained in part a for the first 8 hours? (5 points)

Assume that the velocity is a linear function of time, so that
v(t) = a + bt
where
v = velocity (km/h) at time t (hours),
a and b are constants.

When t = 2 hours, v = 18 km/h, therefore
a + 2b = 18         (1)

When t = 4 hours,  v = 4 km/h, therefore
a + 4b = 4          (2)

Subtract (1) from (2) to obtain
a + 4b - (a + 2b) = 4 - 18
2b = -14
  b = -7
From (1), obtain
a = 18 - 2b = 18 - 2*(-7) = 32

Part A.
The equation is
v = 32 - 7t

Part B
To graph the equation for the first 8 hours, create a table as shown below.
t, hours:   0    1    2   3   4   5    6    7    8
v, km/h:  32 25  18  11   4  -3  -10 -17 -24

We can see from the table that the velocity becomes negative between t=4 and t=5. Therefore, we shall change all negative velocities to zero, and assume that the cyclist comes to rest.
TNote that when the velocity is zero,
 32 - 7t = 0
 7t = 32
t = 4.57

The new table becomes
t:    0   1    2   3   4  4.57  5   6   7   8
v: 32 25  18  11   4   0      0   0   0   0
 
The graph is shown below.