select the correct answer.

lance is knitting a blanket and needs to buy some more yarn. at his local craft store, 2 balls of yarn cost \$5 and 8 balls of yarn cost \$20. what is the constant of proportionality in this direct variation situation?

* $\frac{5}{2}$
* $\frac{2}{5}$
* 5
* 2

Question

select the correct answer.

lance is knitting a blanket and needs to buy some more yarn. at his local craft store, 2 balls of yarn cost \$5 and 8 balls of yarn cost \$20. what is the constant of proportionality in this direct variation situation?

* $\frac{5}{2}$
* $\frac{2}{5}$
* 5
* 2

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Direct Variation" ], "new_concepts": [], "current_concepts": [ "Direct Variation", "Constant of Proportionality" ] } ## Identify the variables and direct variation relationship $$ \begin{aligned} &y = \text{cost in dollars} \ &x = \text{number of balls of yarn} \ &y = kx \end{aligned} $$ ## Calculate the constant of proportionality $$ \begin{aligned} &5 = k \cdot 2 \ &k = \frac{5}{2} \end{aligned} $$ ## Verify with the second data point $$ \begin{aligned} &20 = \frac{5}{2} \cdot 8 \ &20 = 20 \end{aligned} $$

(A) $\frac{5}{2}$

(B) $\frac{2}{5}$

(C) 5

(D) 2

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Direct Variation" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the variables and direct variation relationship

Calculate the constant of proportionality

Verify with the second data point

Answer: