Based on the description provided about the graph of the laptop loan, here are the true statements:
-
The y-intercept is (0, 1000) and shows that at 0 time, your loan is $1000.
This statement is true because at the start (0 weeks), the amount owed is indeed $1000. -
The slope of the graph shows a decrease of $100 in a 10 week period of time.
This is true because the person pays off $100 over the course of 10 weeks, which indicates a total decrease of $100. -
The graph is decreasing with a constant rate of change.
This is also true, as the loan amount decreases by a fixed amount ($100) over a consistent time period (10 weeks). -
The graph is Linear.
This is true since the payment is consistent, and the relationship between the amount owed and the time taken is linear.
The false statements can be identified as follows:
- "The slope of the graph has a length of 100." (Misleading, since slope refers to the rate of change, not a segment length.)
- "The graph is nonlinear." (False, it is linear.)
- "The slope of the graph shows a decrease of $100 each week." (False, the total decrease is $100 over 10 weeks, which means $10 per week.)
- "The graph is increasing at a constant rate of change." (False, it's decreasing.)
- "The slope of the graph shows that as the weeks increase, the loan also increases." (False, it's decreasing.)
- "The x-intercept is (10, 0) and states that at 0 time, your loan is $10." (False, the x-intercept represents the time taken to pay off the loan, which is when the amount owed is $0, not $10.)
- "The graph is decreasing, but the rate of change does not stay constant." (False, the rate of change is constant.)
Thus, the true statements are:
- The y-intercept is (0, 1000) and shows that at 0 time, your loan is $1000.
- The slope of the graph shows a decrease of $100 in a 10 week period of time.
- The graph is decreasing with a constant rate of change.
- The graph is Linear.
5 answers