Ryan is tracking how much money he has each week.

Question

He started with $50.
He saves $15 per week for the first 6 weeks.
He spent $10 per week after week 6 until the money's all spent.
(4 points)
1) The graph of this scenario would be
because the rate of change changes.

2) The y-intercept of this graph would be
meaning
.

3) The rate of change is
after the first 6 weeks because as the weeks increase the money decreases

Answer 1

Let's break down the scenario step by step:

1. The graph of this scenario would be piecewise linear because the rate of change changes.

   • For the first 6 weeks, Ryan's money increases because he's saving money, creating a line with a positive slope. After week 6, however, Ryan begins to spend money, creating a line with a negative slope, which is why the overall graph is piecewise.

2. The y-intercept of this graph would be 50 meaning Ryan started with $50.

   • The y-intercept of the graph represents the starting amount of money Ryan has before any savings or spending begins.

3. The rate of change is -10 after the first 6 weeks because as the weeks increase the money decreases.

   • After week 6, for each week, Ryan loses $10, resulting in a negative rate of change.

In summary:

1. The graph is piecewise linear.
2. The y-intercept is 50, meaning he starts with $50.
3. The rate of change is -10 after the first 6 weeks.