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", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Slope of a Line", "Parallel Line Equations", "Point-Slope Form" ], "new_concepts": [], "current_concepts": [ "Slope of a Line", "Parallel Line Equations", "Point-Slope Form" ] } ## Find the slope of the given line Using the *Slope of a Line* knowledge point $$ \begin{aligned} &(x_1, y_1) = (-2, -4),\quad (x_2, y_2) = (2, 2)\ &m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - (-4)}{2 - (-2)} = \frac{6}{4} = \frac{3}{2} \end{aligned} $$ ## Determine the slope of the parallel line Using the *Parallel Line Equations* knowledge point $$ \begin{aligned} &m_{\text{parallel}} = m = \frac{3}{2} \end{aligned} $$ ## Write the equation in point-slope form Using the *Point-Slope Form* knowledge point $$ \begin{aligned} &(x_0, y_0) = (-3, 1),\quad m_{\text{parallel}} = \frac{3}{2}\ &y - y_0 = m_{\text{parallel}}(x - x_0)\ &y - 1 = \frac{3}{2}(x - (-3))\ &y - 1 = \frac{3}{2}(x + 3) \end{aligned} $$

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

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QUESTION IMAGE

Question

Explanation:

Find the slope of the given line

Determine the slope of the parallel line

Write the equation in point-slope form

Answer: