Question

which table shows a proportional relationship between x and y?
x: 40, 50, 60, 90
y: 8, 10, 14, 18
x: 1, 2, 3, 4
y: 6, 8, 10, 12
x: 2, 4, 7, 8
y: 6, 10, 21, 24
x: 4, 7, 8, 10
y: 2, 3.5, 4, 5
options: chart b, chart a, chart c, chart d

Explanation:

Step1: Define proportional relationship

A proportional relationship means $\frac{y}{x} = k$ (constant) for all pairs.

Step2: Check Chart A

Calculate $\frac{y}{x}$ for each pair:
$\frac{8}{40}=0.2$, $\frac{10}{50}=0.2$, $\frac{14}{60}\approx0.233$, $\frac{18}{90}=0.2$
Not all ratios equal, so not proportional.

Step3: Check Chart B

Calculate $\frac{y}{x}$ for each pair:
$\frac{6}{1}=6$, $\frac{8}{2}=4$, $\frac{10}{3}\approx3.33$, $\frac{12}{4}=3$
Ratios are not equal, so not proportional.

Step4: Check Chart C

Calculate $\frac{y}{x}$ for each pair:
$\frac{6}{2}=3$, $\frac{10}{4}=2.5$, $\frac{21}{7}=3$, $\frac{24}{8}=3$
Ratios are not equal, so not proportional.

Step5: Check Chart D

Calculate $\frac{y}{x}$ for each pair:
$\frac{2}{4}=0.5$, $\frac{3.5}{7}=0.5$, $\frac{4}{8}=0.5$, $\frac{5}{10}=0.5$
All ratios are equal to 0.5, so this is proportional.

Answer:

D. Chart D