what is the equation of the line that is parallel to the given line and passes through the point $(-3, 2)$?

$3x - 4y = -17$
$3x - 4y = -20$
$4x + 3y = -2$
$4x + 3y = -6$

Question

what is the equation of the line that is parallel to the given line and passes through the point $(-3, 2)$?

$3x - 4y = -17$
$3x - 4y = -20$
$4x + 3y = -2$
$4x + 3y = -6$

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 $$ \begin{aligned} &(x_1, y_1) = (0, 3),\quad (x_2, y_2) = (3, -1)\ &m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - 3}{3 - 0} = -\frac{4}{3} \end{aligned} $$ ## Determine the slope of the parallel line Using the *Parallel Line Equations* knowledge point $$ \begin{aligned} &m_{\text{parallel}} = m = -\frac{4}{3} \end{aligned} $$ ## Write the equation in point-slope form Using the *Point-Slope Form* knowledge point $$ \begin{aligned} &(x_0, y_0) = (-3, 2)\ &y - y_0 = m_{\text{parallel}}(x - x_0)\ &y - 2 = -\frac{4}{3}(x - (-3))\ &y - 2 = -\frac{4}{3}(x + 3) \end{aligned} $$ ## Convert to standard form Using the *Parallel Line Equations* knowledge point $$ \begin{aligned} &3(y - 2) = -4(x + 3)\ &3y - 6 = -4x - 12\ &4x + 3y = -6 \end{aligned} $$

(A) $3x - 4y = -17$

(B) $3x - 4y = -20$

(C) $4x + 3y = -2$

(D) $4x + 3y = -6$

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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

Convert to standard form

Answer: