darren is finding the equation in the form $y = mx + b$ for a trend line that passes through the points $(2, 18)$ and $(-3, 8)$.
which value should he use as $b$ in his equation?

-34
-19
2
14

Question

darren is finding the equation in the form $y = mx + b$ for a trend line that passes through the points $(2, 18)$ and $(-3, 8)$.
which value should he use as $b$ in his equation?

-34
-19
2
14

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [], "current_concepts": [ "Slope-Intercept Form", "Linear Modeling", "Trend Line Estimation" ] } ## Calculate the slope of the trend line $$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 18}{-3 - 2} = \frac{-10}{-5} = 2 $$ ## Solve for the y-intercept b $$ \begin{aligned} y &= mx + b \ 18 &= 2(2) + b \ 18 &= 4 + b \ b &= 14 \end{aligned} $$

(A) $-34$

(B) $-19$

(C) $2$

(D) $14$

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

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QUESTION IMAGE

Question

Explanation:

Calculate the slope of the trend line

Solve for the y-intercept b

Answer: