Direct variation

Question

The ordered pairs (3,-1),(6,-2) and (9,-3) are in the form (s,t) represents the time in seconds needed to download an Internet file of size s(in megabytes). Tell whether the data shows a direct variation. If so write an equation that related s and t 

Answer 1

The points are:

(3,-1)

(6,-2)

(9,-3)

 

From the first point to the second, y decreases by 1 as x increases by 3.

From the second point to the third, y decreases by 1 as x increases by 3.

 

This describes a line with slope of (-1/3).  That means the (m) = (-1/3) in the formula y = mx + b.

 

Now, use either point to determine the value of b.

      -1 = (-1/3)(3) + b

      -1 = -1 + b

       0 = b     (this is the y-intercept, the value of y when x=0)

 

So, the formula that relates s to t is:

    t = (-1/3)s