a daycare facility charges a fee for every minute that a parent is late after the facilitys published closing time. the table represents the fee, $y$, which is dependent on the number of minutes late, $x$.

which of the following linear equations represents the situation?

$y = 3x + 22$
$y = 6x + 36$
$y = 6x + 2$
$y = 24x + 36$

Question

a daycare facility charges a fee for every minute that a parent is late after the facilitys published closing time. the table represents the fee, $y$, which is dependent on the number of minutes late, $x$.

which of the following linear equations represents the situation?

$y = 3x + 22$
$y = 6x + 36$
$y = 6x + 2$
$y = 24x + 36$

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 of a Line", "Slope-Intercept Form" ], "new_concepts": [], "current_concepts": [ "Slope of a Line", "Slope-Intercept Form", "Linear Equation Solving" ] } ## Calculate the rate of change Using the *Slope of a Line* knowledge point $$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{50 - 32}{8 - 5} = \frac{18}{3} = 6 $$ ## Determine the y-intercept Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} y &= mx + b\ 32 &= 6(5) + b\ 32 &= 30 + b\ b &= 2 \end{aligned} $$ ## Formulate the linear equation Using the *Slope-Intercept Form* knowledge point $$ y = 6x + 2 $$

(A) $y = 3x + 22$

(B) $y = 6x + 36$

(C) $y = 6x + 2$

(D) $y = 24x + 36$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Slope-Intercept Form" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the rate of change

Determine the y-intercept

Formulate the linear equation

Answer: