which equations represent functions?

$2x + 3y = 10$

$4x = 16$

$2x - 3 = 14$

$3y = 18$

$14.6 = 2x$

Question

which equations represent functions?

$2x + 3y = 10$

$4x = 16$

$2x - 3 = 14$

$3y = 18$

$14.6 = 2x$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Function Definition" ], "new_concepts": [], "current_concepts": [ "Function Definition", "Relations and Functions" ] } ## Analyze equations with both variables $$ \begin{aligned} &2x + 3y = 10 \implies y = -\frac{2}{3}x + \frac{10}{3} \end{aligned} $$ ## Analyze equations with only one variable $$ \begin{aligned} &4x = 16 \implies x = 4 \quad (\text{vertical line, not a function})\ &2x - 3 = 14 \implies x = 8.5 \quad (\text{vertical line, not a function})\ &3y = 18 \implies y = 6 \quad (\text{horizontal line, is a function})\ &14.6 = 2x \implies x = 7.3 \quad (\text{vertical line, not a function}) \end{aligned} $$

[x] $2x + 3y = 10$

[ ] $4x = 16$

[ ] $2x - 3 = 14$

[x] $3y = 18$

[ ] $14.6 = 2x$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Function Definition" ] }

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Question

Explanation:

Analyze equations with both variables

Analyze equations with only one variable

Answer: