considering only functions with a greater rate of change than that of the function represented on the graph, which function has the lowest rate of change?

$y = \frac{13}{9}x - \frac{7}{9}$
$y = \frac{7}{5}x + \frac{3}{5}$
$y = \frac{11}{8}x + \frac{3}{8}$
$y = \frac{5}{4}x + \frac{11}{4}$
$y = \frac{8}{5}x - \frac{4}{5}$

Question

considering only functions with a greater rate of change than that of the function represented on the graph, which function has the lowest rate of change?

$y = \frac{13}{9}x - \frac{7}{9}$
$y = \frac{7}{5}x + \frac{3}{5}$
$y = \frac{11}{8}x + \frac{3}{8}$
$y = \frac{5}{4}x + \frac{11}{4}$
$y = \frac{8}{5}x - \frac{4}{5}$

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 Line", "Rate of Change Analysis" ], "new_concepts": [], "current_concepts": [ "Slope of a Line", "Rate of Change Analysis" ] } ## Find the rate of change of the graphed function $$ \begin{aligned} &\text{Point 1: } (1, -1) \ &\text{Point 2: } (5, 4) \ &m_{\text{graph}} = \frac{4 - (-1)}{5 - 1} = \frac{5}{4} = 1.25 \end{aligned} $$ ## Identify rates of change of the options $$ \begin{aligned} &m_1 = \frac{13}{9} \approx 1.44 \ &m_2 = \frac{7}{6} \approx 1.17 \ &m_3 = \frac{11}{8} \approx 1.375 \ &m_4 = \frac{5}{4} = 1.25 \ &m_5 = \frac{8}{5} = 1.6 \end{aligned} $$ ## Filter and select the lowest rate of change greater than the graph's rate $$ \begin{aligned} &\text{Condition: } m > 1.25 \ &\text{Valid options: } m_1 \approx 1.44, \quad m_3 = 1.375, \quad m_5 = 1.6 \ &\text{Lowest among valid: } m_3 = \frac{11}{8} = 1.375 \end{aligned} $$

$y = \frac{13}{9}x - \frac{7}{9}$

$y = \frac{7}{6}x + \frac{1}{6}$

$y = \frac{11}{8}x + \frac{3}{8}$

$y = \frac{5}{4}x + \frac{11}{4}$

$y = \frac{8}{5}x - \frac{4}{5}$

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

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QUESTION IMAGE

Question

Explanation:

Find the rate of change of the graphed function

Identify rates of change of the options

Filter and select the lowest rate of change greater than the graph's rate

Answer: