a given line has the equation $10x+2y=-2$.

what is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point $(0, 12)$?

$\bigcirc$ $y=-5x+12$
$\bigcirc$ $5x+y=12$
$\bigcirc$ $y-12=5(x-0)$
$\bigcirc$ $5x+y=-1$

Question

a given line has the equation $10x+2y=-2$.

what is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point $(0, 12)$?

$\bigcirc$ $y=-5x+12$
$\bigcirc$ $5x+y=12$
$\bigcirc$ $y-12=5(x-0)$
$\bigcirc$ $5x+y=-1$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Slope-Intercept Form", "Linear Equations" ], "new_concepts": [ "Parallel Lines Slope" ], "current_concepts": [ "Slope-Intercept Form", "Linear Equations", "Parallel Lines Slope" ] } ## Find the slope of the given line $$ \begin{aligned} 10x + 2y &= -2 \ 2y &= -10x - 2 \ y &= -5x - 1 \end{aligned} $$ $$ m = -5 $$ ## Determine the equation of the parallel line $$ \begin{aligned} m_{\text{parallel}} &= -5 \ (x_1, y_1) &= (0, 12) \ y - 12 &= -5(x - 0) \ y &= -5x + 12 \end{aligned} $$

(A) $y=-5x+12$

(B) $5x+y=12$

(C) $y-12=5(x-0)$

(D) $5x+y=-1$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Find the slope of the given line

Determine the equation of the parallel line

Answer: