sam and sully are electricians. the graph represents the amount in dollars that sam charges in terms of the number of hours he works.

the amount in dollars that sully charges in terms of the number of hours he works is represented by the function $y = 22x + 36$.

the initial amount sam charges is choose an answer the initial amount sully charges. sams hourly rate is choose an answer sullys hourly rate.

Question

sam and sully are electricians. the graph represents the amount in dollars that sam charges in terms of the number of hours he works.

the amount in dollars that sully charges in terms of the number of hours he works is represented by the function $y = 22x + 36$.

the initial amount sam charges is choose an answer the initial amount sully charges. sams hourly rate is choose an answer sullys hourly rate.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Slope of a Line", "Linear Graphs", "Comparing Linear Functions" ], "new_concepts": [], "current_concepts": [ "Slope of a Line", "Linear Graphs", "Comparing Linear Functions" ] } ## Determine Sam's initial charge and hourly rate from the graph $$ \begin{aligned} &\text{Initial charge (} y \text{-intercept at } x = 0\text{): } y_0 = 40 \ &\text{Point on the line: } (3, 100) \ &\text{Hourly rate (slope): } m_{\text{Sam}} = \frac{100 - 40}{3 - 0} = \frac{60}{3} = 20 \end{aligned} $$ ## Determine Sully's initial charge and hourly rate from the equation $$ \begin{aligned} &y = 22x + 36 \ &\text{Initial charge: } 36 \ &\text{Hourly rate: } 22 \end{aligned} $$ ## Compare the initial charges and hourly rates $$ \begin{aligned} &\text{Initial charge: } 40 > 36 \implies \text{greater than} \ &\text{Hourly rate: } 20 < 22 \implies \text{less than} \end{aligned} $$ The initial amount Sam charges is greater than the initial amount Sully charges. Sam's hourly rate is less than Sully's hourly rate. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Comparing Linear Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Determine Sam's initial charge and hourly rate from the graph

Determine Sully's initial charge and hourly rate from the equation

Compare the initial charges and hourly rates

Answer: