select all of the following that are linear functions.

$x = 5$

$\begin{array}{|c|c|}\hline x & y \\\hline -2 & 4 \\\hline 0 & 1 \\\hline 2 & -2 \\\hline 4 & 5 \\\hline\end{array}$

$x + 7 = 4y$

Question

select all of the following that are linear functions.

$x = 5$

$\begin{array}{|c|c|}\hline x & y \\\hline -2 & 4 \\\hline 0 & 1 \\\hline 2 & -2 \\\hline 4 & 5 \\\hline\end{array}$

$x + 7 = 4y$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear Functions" ], "new_concepts": [], "current_concepts": [ "Linear Functions", "Slope-Intercept Form" ] } ## Analyze the given options for linearity and function definition $$ \begin{aligned} &\text{Option 1: } x = 5 \ &\quad \text{This represents a vertical line, which fails the vertical line test and is not a function.} \ &\text{Option 2: Table of values } (-2, 4), (0, 1), (2, -2), (4, 5) \ &\quad \text{Rate of change on } [-2, 0]: \frac{1 - 4}{0 - (-2)} = -1.5 \ &\quad \text{Rate of change on } [2, 4]: \frac{5 - (-2)}{4 - 2} = 3.5 \ &\quad \text{The rate of change is not constant, so it is not linear.} \ &\text{Option 3: } x + 7 = 4y \ &\quad y = \frac{1}{4}x + \frac{7}{4} \ &\quad \text{This is in slope-intercept form } y = mx + b \text{, representing a linear function.} \ &\text{Option 4: Graph of a straight line} \ &\quad \text{The graph shows a non-vertical straight line, which represents a linear function.} \end{aligned} $$

(A) $x = 5$

(B) The table with points $(-2, 4)$, $(0, 1)$, $(2, -2)$, and $(4, 5)$

(C) $x + 7 = 4y$

(D) The graph showing a non-vertical straight line

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Linear Functions" ] }

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Explanation:

Analyze the given options for linearity and function definition

Answer: