which of these linear equations best describes the given model?

choose 1 answer:
(a) $\hat{y} = x + 0.25$
(b) $\hat{y} = x + 0.5$
(c) $\hat{y} = 0.5x + 0.25$

Question

which of these linear equations best describes the given model?

choose 1 answer:
(a) $\hat{y} = x + 0.25$
(b) $\hat{y} = x + 0.5$
(c) $\hat{y} = 0.5x + 0.25$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Line of Best Fit", "Slope Estimation" ], "new_concepts": [], "current_concepts": [ "Line of Best Fit", "Slope Estimation", "Scatter Plots" ] } ## Identify the y-intercept $$ \begin{aligned} &\text{At } x = 0, \text{ the line intersects the y-axis at } y = 0.25. \end{aligned} $$ ## Calculate the slope $$ \begin{aligned} &\text{Using points } (0, 0.25) \text{ and } (4, 2.25):\ &m = \frac{2.25 - 0.25}{4 - 0} = \frac{2}{4} = 0.5 \end{aligned} $$ ## Formulate the linear equation $$ \begin{aligned} &\hat{y} = mx + b\ &\hat{y} = 0.5x + 0.25 \end{aligned} $$

(A) $\hat{y} = x + 0.25$

(B) $\hat{y} = x + 0.5$

(C) $\hat{y} = 0.5x + 0.25$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Line of Best Fit" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the y-intercept

Calculate the slope

Formulate the linear equation

Answer: