Question

Elena agrees to finish a knitting project for a friend. The graph shows the number of rows Elena completes compared to the amount of time spent knitting.
Assuming she worked at a constant rate, how many rows had been completed before Elena started working?
12
14
15
19

Answer 1

The answer is 12. :)

Answer 2

First of all, using the information about constant rate we can say that these points are located on a straight line. Indeed, the logic is about a constant rate. Then, we can easily claim that the points are located on a quasi-linear function, y=kx+b. We could solve this problem by setting up a system of equations. The system is this:

$\left \{ {{19=14k+b} \atop {22=20k+b}} \right.$

By solving it, we find that k=0.5 and b=12. Then the function is y=0.5x+12

We have to find that how many rows were completed, before Elene started, i.e, x = 0. Then y=0.5*0+12 = 12. The answer is 12 rows.