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Graphs, Functions, and Sequences
Identifying proportional relationships in tables by calculating unit rates:...
For each table, determine whether it shows that 
x and 
y are proportional.
If 
x and 
y are proportional, fill in the blank with a number in simplest form.




Table 1
Table 2



x
18
24
7

x
3
4
7


3
4
42

y
6
12
28


Proportional
Proportional



y is 
◻ times 
x

y is 
◻ times 
x


Not proportional
Not proportional

Graphs, Functions, and Sequences\newlineIdentifying proportional relationships in tables by calculating unit rates:...\newlineFor each table, determine whether it shows that x x and y y are proportional.\newlineIf x x and y y are proportional, fill in the blank with a number in simplest form.\newline\begin{tabular}{|c|c|c|c|c|c|c|c|}\newline\hline \multicolumn{44}{|c|}{ Table 11} & \multicolumn{44}{|c|}{ Table 22} \\\newline\hline \multirow[t]{22}{*}{x x } & 1818 & 2424 & 77 & x x & 33 & 44 & 77 \\\newline\hline & 33 & 44 & 4242 & y y & 66 & 1212 & 2828 \\\newline\hline \multicolumn{44}{|c|}{ Proportional } & \multicolumn{44}{|c|}{ Proportional } \\\newline\hline \multicolumn{44}{|c|}{y y is \square times x x } & \multicolumn{44}{|c|}{y y is \square times x x } \\\newline\hline \multicolumn{44}{|c|}{ Not proportional } & \multicolumn{44}{|c|}{ Not proportional } \\\newline\hline\newline\end{tabular}

Full solution

Q. Graphs, Functions, and Sequences\newlineIdentifying proportional relationships in tables by calculating unit rates:...\newlineFor each table, determine whether it shows that x x and y y are proportional.\newlineIf x x and y y are proportional, fill in the blank with a number in simplest form.\newline\begin{tabular}{|c|c|c|c|c|c|c|c|}\newline\hline \multicolumn{44}{|c|}{ Table 11} & \multicolumn{44}{|c|}{ Table 22} \\\newline\hline \multirow[t]{22}{*}{x x } & 1818 & 2424 & 77 & x x & 33 & 44 & 77 \\\newline\hline & 33 & 44 & 4242 & y y & 66 & 1212 & 2828 \\\newline\hline \multicolumn{44}{|c|}{ Proportional } & \multicolumn{44}{|c|}{ Proportional } \\\newline\hline \multicolumn{44}{|c|}{y y is \square times x x } & \multicolumn{44}{|c|}{y y is \square times x x } \\\newline\hline \multicolumn{44}{|c|}{ Not proportional } & \multicolumn{44}{|c|}{ Not proportional } \\\newline\hline\newline\end{tabular}
  1. Calculate Ratios: For Table 11, calculate the ratio of yy to xx for each pair to see if it's constant.\newlineFirst pair: 318=16\frac{3}{18} = \frac{1}{6}\newlineSecond pair: 424=16\frac{4}{24} = \frac{1}{6}\newlineThird pair: 427=6\frac{42}{7} = 6

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