question 6 points 2

which function has a greater rate of change?

$y = 2 - 0.9x$

$2y = 4x + 5$

Question

question 6 points 2

which function has a greater rate of change?

$y = 2 - 0.9x$

$2y = 4x + 5$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Slope of a Linear Function", "Slope-Intercept Form" ], "new_concepts": [ "Rate of Change Comparison" ], "current_concepts": [ "Slope of a Linear Function", "Slope-Intercept Form", "Rate of Change Comparison" ] } ## Find the rate of change of the first function $$ \begin{aligned} &y = 2 - 0.9x \ &y = -0.9x + 2 \ &m_1 = -0.9 \ &\text{Rate of change (magnitude)} = |-0.9| = 0.9 \end{aligned} $$ ## Find the rate of change of the second function $$ \begin{aligned} &2y = 4x + 5 \ &y = 2x + 2.5 \ &m_2 = 2 \ &\text{Rate of change (magnitude)} = |2| = 2 \end{aligned} $$ ## Compare the rates of change $$ \begin{aligned} &2 > 0.9 \ &\text{The function } 2y = 4x + 5 \text{ has a greater rate of change.} \end{aligned} $$

$y = 2 - 0.9x$

$2y = 4x + 5$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Slope of a Linear Function" ] }

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QUESTION IMAGE

Question

Explanation:

Find the rate of change of the first function

Find the rate of change of the second function

Compare the rates of change

Answer: