what is the equation of the line that is parallel to the line (y - 1 = 4(x + 3)) and passes through the point ((4, 32))?

(y = -\frac{1}{4}x + 33)
(y = -\frac{1}{4}x + 36)
(y = 4x - 16)
(y = 4x + 16)

Question

what is the equation of the line that is parallel to the line (y - 1 = 4(x + 3)) and passes through the point ((4, 32))?

(y = -\frac{1}{4}x + 33)
(y = -\frac{1}{4}x + 36)
(y = 4x - 16)
(y = 4x + 16)

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", "Slope-Intercept Form" ], "new_concepts": [], "current_concepts": [ "Parallel Lines Slope", "Point-Slope Form", "Slope-Intercept Form", "Linear Equations" ] } ## Determine the slope of the parallel line $$ \begin{aligned} &y - 1 = 4(x + 3) \ &m = 4 \end{aligned} $$ ## Write the equation in point-slope form $$ \begin{aligned} &(x_1, y_1) = (4, 32) \ &y - 32 = 4(x - 4) \end{aligned} $$ ## Convert to slope-intercept form $$ \begin{aligned} &y - 32 = 4x - 16 \ &y = 4x + 16 \end{aligned} $$

(A) $y = -\frac{1}{4}x + 33$

(B) $y = -\frac{1}{4}x + 36$

(C) $y = 4x - 16$

(D) $y = 4x + 16$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Parallel Lines Slope" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Determine the slope of the parallel line

Write the equation in point-slope form

Convert to slope-intercept form

Answer: