mark and jessica are each making a linear model to predict the population of squirrels in the town park. they are both using the same data points to find an equation of the line of best fit: the squirrel population, (p), in 2002 and the squirrel population, (q), in 2011. mark is using the year as the (x)-value, and he represents his data as ((2002, p)) and ((2011, q)). jessica is using the years since 2000 as her (x)-value, and she represents her data as ((2, p)) and ((11, q)). which statement best describes how their prediction equations compare?

their equations have the same slopes and y-intercepts.
their equations have different slopes and y-intercepts.
their equations have different y-intercepts but the same slopes.
their equations have the same y-intercepts but different slopes.

Question

mark and jessica are each making a linear model to predict the population of squirrels in the town park. they are both using the same data points to find an equation of the line of best fit: the squirrel population, (p), in 2002 and the squirrel population, (q), in 2011. mark is using the year as the (x)-value, and he represents his data as ((2002, p)) and ((2011, q)). jessica is using the years since 2000 as her (x)-value, and she represents her data as ((2, p)) and ((11, q)). which statement best describes how their prediction equations compare?

their equations have the same slopes and y-intercepts.
their equations have different slopes and y-intercepts.
their equations have different y-intercepts but the same slopes.
their equations have the same y-intercepts but different slopes.

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-Intercept Form", "Linear Modeling" ], "new_concepts": [ "Linear Transformations", "Horizontal Translation" ], "current_concepts": [ "Slope-Intercept Form", "Linear Modeling", "Linear Transformations", "Horizontal Translation" ] } ## Compare the slopes of both models Using the *Slope-Intercept Form* and *Linear Modeling* knowledge points $$ \begin{aligned} m_{\text{Mark}} &= \frac{q - p}{2011 - 2002} = \frac{q - p}{9} \ m_{\text{Jessica}} &= \frac{q - p}{11 - 2} = \frac{q - p}{9} \ m_{\text{Mark}} &= m_{\text{Jessica}} \end{aligned} $$ ## Compare the y-intercepts of both models Using the *Slope-Intercept Form* and *Linear Modeling* knowledge points $$ \begin{aligned} y - y_1 &= m(x - x_1) \ b_{\text{Mark}} &= p - m(2002) \ b_{\text{Jessica}} &= p - m(2) \ b_{\text{Mark}} & e b_{\text{Jessica}} \quad (\text{since } 2002 e 2 \text{ and } m e 0) \end{aligned} $$

Their equations have the same slopes and y-intercepts.

Their equations have different slopes and y-intercepts.

Their equations have different y-intercepts but the same slopes.

Their equations have the same y-intercepts but different slopes.

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

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QUESTION IMAGE

Question

Explanation:

Compare the slopes of both models

Compare the y-intercepts of both models

Answer: