Question

Question content area top
Part 1
Decide whether the table shows a proportional relationship between x and y.
x
y
30
150
one sixth
five sixths
199
995
two fifteenths
two thirds
Question content area bottom
Part 1
The table
▼
does
does not
show a proportional relationship between x and y.

Answer 1

To determine if the table shows a proportional relationship between \( x \) and \( y \), you need to check if the ratios \( \frac{y}{x} \) are the same for all pairs of \( (x, y) \).

Let's calculate the ratios for each pair:

1. For \( x = 30 \) and \( y = 150 \):
\[
\frac{y}{x} = \frac{150}{30} = 5
\]

2. For \( x = \frac{1}{6} \) and \( y = \frac{5}{6} \):
\[
\frac{y}{x} = \frac{\frac{5}{6}}{\frac{1}{6}} = 5
\]

3. For \( x = 199 \) and \( y = 995 \):
\[
\frac{y}{x} = \frac{995}{199} = 5
\]

4. For \( x = \frac{2}{15} \) and \( y = \frac{2}{3} \):
\[
\frac{y}{x} = \frac{\frac{2}{3}}{\frac{2}{15}} = \frac{2}{3} \times \frac{15}{2} = 5
\]

Since all the ratios \( \frac{y}{x} \) are equal (all equal to 5), the table does show a proportional relationship.

Therefore, the table **does** show a proportional relationship between \( x \) and \( y \).