the equation $y + 6 = \frac{1}{3}(x - 9)$ is written in point-slope form. what is the equation written in slope-intercept form?

$y = \frac{1}{3}x - 3$
$y = \frac{1}{3}x + 9$
$y = \frac{1}{3}x - 9$
$y = \frac{1}{3}x + 3$

Question

the equation $y + 6 = \frac{1}{3}(x - 9)$ is written in point-slope form. what is the equation written in slope-intercept form?

$y = \frac{1}{3}x - 3$
$y = \frac{1}{3}x + 9$
$y = \frac{1}{3}x - 9$
$y = \frac{1}{3}x + 3$

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": [ "Point-Slope Form", "Slope-Intercept Form" ], "new_concepts": [], "current_concepts": [ "Point-Slope Form", "Slope-Intercept Form", "Linear Equation Modeling" ] } ## Identify the given equation and target form Using the *Point-Slope Form* knowledge point $$ y + 6 = \frac{1}{3}(x - 9) $$ ## Distribute the slope on the right side Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} y + 6 &= \frac{1}{3}x - \frac{1}{3}(9) \ y + 6 &= \frac{1}{3}x - 3 \end{aligned} $$ ## Isolate y to find the final equation Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} y &= \frac{1}{3}x - 3 - 6 \ y &= \frac{1}{3}x - 9 \end{aligned} $$

(A) $y = \frac{1}{3}x - 3$

(B) $y = \frac{1}{3}x + 9$

(C) $y = \frac{1}{3}x - 9$

(D) $y = \frac{1}{3}x + 3$

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

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QUESTION IMAGE

Question

Explanation:

Identify the given equation and target form

Distribute the slope on the right side

Isolate y to find the final equation

Answer: