find the function which has lesser rate of change.

$3x + y = 9$

$x - y = 5$

Question

find the function which has lesser rate of change.

$3x + y = 9$

$x - y = 5$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Slope-Intercept Form", "Slope of a Linear Function", "Rate of Change Comparison" ], "new_concepts": [], "current_concepts": [ "Slope-Intercept Form", "Slope of a Linear Function", "Rate of Change Comparison" ] } ## Find the rate of change of the first function Using the *Slope-Intercept Form* and *Slope of a Linear Function* knowledge points $$ \begin{aligned} 3x + y &= 9 \ y &= -3x + 9 \ m_1 &= -3 \end{aligned} $$ ## Find the rate of change of the second function Using the *Slope-Intercept Form* and *Slope of a Linear Function* knowledge points $$ \begin{aligned} x - y &= 5 \ -y &= -x + 5 \ y &= x - 5 \ m_2 &= 1 \end{aligned} $$ ## Compare the rates of change Using the *Rate of Change Comparison* knowledge point $$ \begin{aligned} -3 &< 1 \ m_1 &< m_2 \end{aligned} $$

(A) $3x + y = 9$

(B) $x - y = 5$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Rate of Change Comparison" ] }

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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: