Question

a car traveling at 30 meters per second begins to slow down at a constant rate. after 2 seconds its velocity is 16 meters per second. write an equation that represents the cars velocity v after t seconds

Answer 1

Let the acceleration (really deceleration) be a
so v = at + c
when t=0 , v = 30
30 = 0 + c, --> c=30
so v = at + 30
when t=2, v = 16
16 = 2a + 30
2a = -14
a = -7

v = -7t + 30

Answer 2

I just solved your question using Calculus, but I am not sure if you know Calculus, so ....

Treat your data two ordered pairs (0,30) and (2,16)
where the first coordinate is time and the second is velocity
slope = (30-16)/(0-2) = -7
so v = -7t + b , using the old y = mx + b format
but (0,30) must satisfy this
30 = 0 + b
b = 30

so v = -7t + 30 , as before