question 8 of 10

which of the following graphs represents the equation $y - 2 = 3(x - 1)$?

a. graph a
b. graph b
c. graph c
d. graph d

Question

question 8 of 10

which of the following graphs represents the equation $y - 2 = 3(x - 1)$?

a. graph a
b. graph b
c. graph c
d. graph d

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Point-Slope Form", "Linear Equations" ], "new_concepts": [], "current_concepts": [ "Point-Slope Form", "Linear Equations", "Coordinate Geometry" ] } ## Identify point and slope from equation $$ \begin{aligned} &y - y_1 = m(x - x_1) \ &y - 2 = 3(x - 1) \ &(x_1, y_1) = (1, 2) \ &m = 3 \end{aligned} $$ ## Verify points on the correct graph $$ \begin{aligned} &\text{Graph B contains the point } (1, 2) \ &\text{Check } y\text{-intercept } (x = 0): \ &y - 2 = 3(0 - 1) \implies y = -1 \implies (0, -1) \ &\text{Graph B contains both } (1, 2) \text{ and } (0, -1) \end{aligned} $$

A. Graph A

B. Graph B

C. Graph C

D. Graph D

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

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QUESTION IMAGE

Question

Explanation:

Identify point and slope from equation

Verify points on the correct graph

Answer: