Math  /  Algebra

QuestionGraphs, Functions, and Sequences Identifying proportional relationships in tables by calculating unit rates:...
For each table, determine whether it shows that xx and yy are proportional. If xx and yy are proportional, fill In the blank with a number in simplest form. \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline \multicolumn{4}{|l|}{ Table 1} & \multicolumn{4}{|l|}{ Table 2} \\ \hlinexx & 16 & 20 & 9 & xx & 4 & 5 & 9 \\ \hlineyy & 4 & 5 & 36 & yy & 8 & 15 & 36 \\ \hline \multicolumn{4}{|l|}{ Proportional } & \multicolumn{4}{|l|}{ Proportional } \\ \hlineyy is & tim & s xx & & yy is \square & tim & s xx & \\ \hline \multicolumn{4}{|l|}{ Not proportional } & \multicolumn{4}{|l|}{ Not proportional } \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. For two variables xx and yy to be proportional, the ratio yx\frac{y}{x} must be constant for all pairs (x,y)(x, y) in the table.
2. In Table 1, we have pairs (16,4)(16, 4), (20,5)(20, 5), and (9,36)(9, 36).
3. In Table 2, we have pairs (4,8)(4, 8), (5,15)(5, 15), and (9,36)(9, 36).
4. We need to calculate yx\frac{y}{x} for each pair and check if the ratios are the same within each table.

STEP 2

1. Calculate the ratios yx\frac{y}{x} for each pair in Table 1.
2. Determine if the ratios in Table 1 are consistent.
3. Calculate the ratios yx\frac{y}{x} for each pair in Table 2.
4. Determine if the ratios in Table 2 are consistent.
5. Fill in the blanks with the constant ratio if xx and yy are proportional.

STEP 3

Calculate the ratio yx\frac{y}{x} for the first pair in Table 1.
yx for (16,4)=416=14 \frac{y}{x} \text{ for } (16, 4) = \frac{4}{16} = \frac{1}{4}

STEP 4

Calculate the ratio yx\frac{y}{x} for the second pair in Table 1.
yx for (20,5)=520=14 \frac{y}{x} \text{ for } (20, 5) = \frac{5}{20} = \frac{1}{4}

STEP 5

Calculate the ratio yx\frac{y}{x} for the third pair in Table 1.
yx for (9,36)=369=4 \frac{y}{x} \text{ for } (9, 36) = \frac{36}{9} = 4

STEP 6

Compare the ratios calculated for Table 1 to determine if they are consistent.
The ratios are 14\frac{1}{4}, 14\frac{1}{4}, and 44. Since these are not the same, xx and yy are not proportional in Table 1.

STEP 7

Calculate the ratio yx\frac{y}{x} for the first pair in Table 2.
yx for (4,8)=84=2 \frac{y}{x} \text{ for } (4, 8) = \frac{8}{4} = 2

STEP 8

Calculate the ratio yx\frac{y}{x} for the second pair in Table 2.
yx for (5,15)=155=3 \frac{y}{x} \text{ for } (5, 15) = \frac{15}{5} = 3

STEP 9

Calculate the ratio yx\frac{y}{x} for the third pair in Table 2.
yx for (9,36)=369=4 \frac{y}{x} \text{ for } (9, 36) = \frac{36}{9} = 4

STEP 10

Compare the ratios calculated for Table 2 to determine if they are consistent.
The ratios are 22, 33, and 44. Since these are not the same, xx and yy are not proportional in Table 2.
Since neither table shows xx and yy to be proportional, the blanks cannot be filled with a constant ratio.

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