Question

Determining the Effect of a New Initial Value
A graph has time (weeks) on the x-axis, and assignments on the y-axis. An orange line goes through (3, 55) and (6, 40). A blue line goes through (0, 85) and (3, 70).

Jenna’s science teacher changed the number of assignments for the semester to 85. This is shown as the blue line on the graph.

How many more weeks will it take Jenna to complete all the assignments if she completes assignments at the same rate?

2
more weeks

Answer 1

The rate is the same for both lines: slope = (70 − 85)/(3 − 0) = −5 assignments/week (and also (40 − 55)/(6 − 3) = −5).

With the original line (start 70): 70 − 5t = 0 ⇒ t = 14 weeks.
With the new start 85: 85 − 5t = 0 ⇒ t = 17 weeks.

So it will take 17 − 14 = 3 more weeks (not 2).