does the following table show a proportional relationship between the variables $x$ and $y$?

$x$ & $\frac{1}{4}$ & $\frac{2}{4}$ & $\frac{3}{4}$
$y$ & 3 & 6 & 9

choose 1 answer:
(a) yes
(b) no

Question

does the following table show a proportional relationship between the variables $x$ and $y$?

$x$ & $\frac{1}{4}$ & $\frac{2}{4}$ & $\frac{3}{4}$
$y$ & 3 & 6 & 9

choose 1 answer:
(a) yes
(b) no

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Constant of Proportionality" ], "new_concepts": [], "current_concepts": [ "Constant of Proportionality", "Proportional Relationships" ] } ## Calculate the ratio of y to x for each pair $$ \begin{aligned} &\text{Pair 1: } \frac{y}{x} = \frac{3}{\frac{1}{4}} = 3 \times 4 = 12\ &\text{Pair 2: } \frac{y}{x} = \frac{6}{\frac{2}{4}} = \frac{6}{\frac{1}{2}} = 6 \times 2 = 12\ &\text{Pair 3: } \frac{y}{x} = \frac{9}{\frac{3}{4}} = 9 \times \frac{4}{3} = 12 \end{aligned} $$ ## Compare the ratios $$ 12 = 12 = 12 $$ ## Determine proportionality $$ \frac{y}{x} = 12 \implies y = 12x $$

(A) Yes

(B) No

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Proportional Relationships" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the ratio of y to x for each pair

Compare the ratios

Determine proportionality

Answer: