Question

other times, the relationship between quantities may take some work to figure out—it can be helpful to first describe in words what you see before trying to nail down an equation in these cases. lets practice this now by looking at several relationships represented by tables of values. remember, tables show values in pairs. as you examine the value pairs in a table, look for any patterns or structures that appear.directionseach of the tables represents a relationship between two quantities $x$ and $y$. describe in words how the quantities in each table are related. then, match each table to the equation that represents the relationship. hint: use the questions above or your list from activity 1 to get jump start your thinking!1. table a| number of taps, $x$ | meters left, $y$ || ---- | ---- || 0 | 0 || 1 | 400 || 2.5 | 1,000 || 6 | 2,400 || 8 | 3,600 |2. table b| meters from home, $x$ | meters from school, $y$ || ---- | ---- || 0 | 400 || 76 | 324 || 128 | 272 || 396 | 4 || 400 | 0 |(hexagon diagram with side length $s$, and table:| side length $s$ | perimeter $p$ || ---- | ---- || 1 | 6 || 2 | 12 || 15 | 90 || 100 | 600 |$p = s + s + s + s + s + s$$p = 6s$)

Explanation:

Step1: Analyze Table A

Check ratio of $y$ to $x$:
$\frac{0}{0}$ (undefined, base case), $\frac{400}{1}=400$, $\frac{1000}{2.5}=400$, $\frac{2400}{6}=400$, $\frac{3600}{9}=400$

Step2: Define Table A relationship

$y$ equals 400 times $x$.
Expression: $y=400x$

Step3: Analyze Table B

Check sum of $x$ and $y$:
$0+400=400$, $76+324=400$, $128+272=400$, $316+84=400$, $396+4=400$

Step4: Define Table B relationship

$y$ equals 400 minus $x$.
Expression: $y=400-x$

Answer:

Table A:

• Relationship: Total meters run is 400 times the number of laps.
• Equation: $y=400x$

Table B:

• Relationship: Meters from school is 400 minus meters from home.
• Equation: $y=400-x$