what is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point $(-3, 1)$?

$y - 1 = -\frac{3}{2}(x + 3)$
$y - 1 = -\frac{2}{3}(x + 3)$
$y - 1 = \frac{2}{3}(x + 3)$
$y - 1 = \frac{3}{2}(x + 3)$

Question

what is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point $(-3, 1)$?

$y - 1 = -\frac{3}{2}(x + 3)$
$y - 1 = -\frac{2}{3}(x + 3)$
$y - 1 = \frac{2}{3}(x + 3)$
$y - 1 = \frac{3}{2}(x + 3)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Parallel Lines Slope", "Point-Slope Form" ], "new_concepts": [], "current_concepts": [ "Parallel Lines Slope", "Point-Slope Form" ] } ## Determine the slope of the given line $$ \begin{aligned} (x_1, y_1) &= (-2, -4) \ (x_2, y_2) &= (2, 2) \ m &= \frac{2 - (-4)}{2 - (-2)} = \frac{6}{4} = \frac{3}{2} \end{aligned} $$ ## Identify the slope of the parallel line $$ m_{\text{parallel}} = m = \frac{3}{2} $$ ## Write the equation in point-slope form $$ \begin{aligned} (x_0, y_0) &= (-3, 1) \ y - y_0 &= m_{\text{parallel}}(x - x_0) \ y - 1 &= \frac{3}{2}(x - (-3)) \ y - 1 &= \frac{3}{2}(x + 3) \end{aligned} $$

(A) $y - 1 = -\frac{3}{2}(x + 3)$

(B) $y - 1 = -\frac{2}{3}(x + 3)$

(C) $y - 1 = \frac{2}{3}(x + 3)$

(D) $y - 1 = \frac{3}{2}(x + 3)$

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

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QUESTION IMAGE

Question

Explanation:

Determine the slope of the given line

Identify the slope of the parallel line

Write the equation in point-slope form

Answer: