if lines joined each given point on the graph to the origin, which points would be on lines that represent a unit rate greater than the one represented in the table?

$\begin{array}{|c|c|}\hline x & y \\\hline 5 & 11 \\\hline 10 & 22 \\\hline 15 & 33 \\\hline\end{array}$

Question

if lines joined each given point on the graph to the origin, which points would be on lines that represent a unit rate greater than the one represented in the table?

$\begin{array}{|c|c|}\hline x & y \\\hline 5 & 11 \\\hline 10 & 22 \\\hline 15 & 33 \\\hline\end{array}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Slope of a Line", "Linear Equations" ], "new_concepts": [ "Unit Rate Comparison" ], "current_concepts": [ "Slope of a Line", "Linear Equations", "Unit Rate Comparison" ] } ## Find the unit rate from the table Using the *Slope of a Line* and *Linear Equations* knowledge points $$ \text{Unit Rate} = \frac{y}{x} = \frac{11}{5} = 2.2 $$ ## Identify coordinates of the plotted points Using the *Slope of a Line* knowledge points $$ \begin{aligned} &\text{Red point 1: } (2, 4)\ &\text{Red point 2: } (4, 8)\ &\text{Blue point 1: } (5, 10)\ &\text{Green point: } (7, 8)\ &\text{Yellow-green point: } (8, 7)\ &\text{Blue point 2: } (9, 6) \end{aligned} $$ ## Calculate unit rates for each point Using the *Slope of a Line* knowledge points $$ \begin{aligned} &\text{Point } (2, 4): \frac{4}{2} = 2.0\ &\text{Point } (4, 8): \frac{8}{4} = 2.0\ &\text{Point } (5, 10): \frac{10}{5} = 2.0\ &\text{Point } (7, 8): \frac{8}{7} \approx 1.14\ &\text{Point } (8, 7): \frac{7}{8} = 0.875\ &\text{Point } (9, 6): \frac{6}{9} \approx 0.67 \end{aligned} $$ ## Compare unit rates to find greater values Using the *Slope of a Line* knowledge points $$ \begin{aligned} &\text{Table rate: } 2.2\ &\text{All plotted points have a unit rate } \le 2.0\ &\text{No points have a unit rate greater than } 2.2 \end{aligned} $$ None of the given points on the graph would be on lines that represent a unit rate greater than the one represented in the table. { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Unit Rate Comparison" ] }

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QUESTION IMAGE

Question

Explanation:

Find the unit rate from the table

Identify coordinates of the plotted points

Calculate unit rates for each point

Compare unit rates to find greater values

Answer: