the scatterplot shows the ages and finishing times of seven men who ran a charity 5k run. use the labeled points to create a linear model that predicts the race time (y) of a man of any age (x). which equation represents this linear model?

$y = 0.47x + 7.72$
$y = 0.47x + 29.15$

Question

the scatterplot shows the ages and finishing times of seven men who ran a charity 5k run. use the labeled points to create a linear model that predicts the race time (y) of a man of any age (x). which equation represents this linear model?

\$y = 0.47x + 7.72\$
\$y = 0.47x + 29.15\$

$y = 0.47x + 7.72$
$y = 0.47x + 29.15$

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": [ "Linear Modeling" ], "new_concepts": [], "current_concepts": [ "Linear Modeling", "Slope-Intercept Form" ] } ## Calculate the slope of the linear model Using the *Linear Modeling* knowledge point $$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{27.25 - 17.5}{43 - 21} = \frac{9.75}{22} \approx 0.443 $$ ## Determine the y-intercept of the linear model Using the *Linear Modeling* knowledge point $$ \begin{aligned} y - y_1 &= m(x - x_1) \ y - 17.5 &= 0.443(x - 21) \ y - 17.5 &= 0.443x - 9.303 \ y &\approx 0.44x + 8.20 \end{aligned} $$ ## Match with the given options Using the *Linear Modeling* knowledge point $$ \begin{aligned} &\text{Option 1: } y = 0.47x + 7.72 \quad (\text{Matches } m \approx 0.44, b \approx 8.20) \ &\text{Option 2: } y = 0.47x + 29.15 \end{aligned} $$

(A) $y = 0.47x + 7.72$

(B) $y = 0.47x + 29.15$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Linear Modeling" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the slope of the linear model

Determine the y-intercept of the linear model

Match with the given options

Answer: