the given line passes through the points $(0, -3)$ and $(2, 3)$.

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

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

Question

the given line passes through the points $(0, -3)$ and $(2, 3)$.

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

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

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Parallel Line Slopes" ], "new_concepts": [ "Point-Slope Form" ], "current_concepts": [ "Parallel Line Slopes", "Point-Slope Form" ] } ## Calculate the slope of the given line $$ m = \frac{3 - (-3)}{2 - 0} = \frac{6}{2} = 3 $$ ## Determine the slope of the parallel line $$ m_{\text{parallel}} = m = 3 $$ ## Write the equation in point-slope form $$ \begin{aligned} &y - y_1 = m(x - x_1) \ &y - (-1) = 3(x - (-1)) \ &y + 1 = 3(x + 1) \end{aligned} $$

(A) $y+1 = -3(x+1)$

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

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

(D) $y+1 = 3(x+1)$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Parallel Line Slopes" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the slope of the given line

Determine the slope of the parallel line

Write the equation in point-slope form

Answer: