Question

activity 3.2 something about 400

1. describe in words how the two quantities in each table are related.

• table a

number of laps, x: 0, 1, 2.5, 6, 9
meters run, y: 0, 400, 1,000, 2,400, 3,600

• table b

meters from home, x: 0, 75, 128, 319, 396
meters from school, y: 400, 325, 272, 81, 4

• table c

electricity bills in dollars, x: 85, 124, 309, 816
total expenses in dollars, y: 485, 524, 709, 1,216

• table d

monthly salary in dollars, x: 872, 998, 1,015, 2,110
amount deposited in dollars, y: 472, 598, 615, 1,710

Explanation:

Step1: Analyze Table A

The number of meters run ($y$) is found by multiplying the number of laps ($x$) by 400. That is, the relationship is $y = 400x$. For example, when $x = 1$, $y=400\times1 = 400$; when $x = 2.5$, $y = 400\times2.5=1000$.

Step2: Analyze Table B

The sum of the meters from home ($x$) and the meters from school ($y$) is always 400. So the relationship is $x + y=400$, or $y = 400 - x$. For example, when $x = 0$, $y=400-0 = 400$; when $x = 75$, $y=400 - 75=325$.

Step3: Analyze Table C

The total expenses ($y$) is the electricity - bill ($x$) plus 400. So the relationship is $y=x + 400$. For example, when $x = 85$, $y=85 + 400=485$; when $x = 124$, $y=124 + 400=524$.

Step4: Analyze Table D

There is no clear relationship related to 400. If we try to find a linear relationship $y=ax + b$, we see that there is no single - value of $a$ and $b$ such that the relationship holds for all data points with 400 involved.

Answer:

Table A: The number of meters run is 400 times the number of laps.
Table B: The sum of the meters from home and the meters from school is 400.
Table C: The total expenses is the electricity bill plus 400.
Table D: No clear relationship related to 400.