Which line is perpendicular to the line -2x + 3y = 12 ?

Question

A. -2x + y = 12

B. y = 2/3 x -1

C. -2x + 3y = 11

D. 3x + 2y = -2

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Answer 1 · 2018-04-08T11:32:55

$D . 3 x + 2 y = - 2$ $color(red)(D. " " 3x + 2y = -2$

Given Equation is $- 2 x + 3 y = 12$ $-2x + 3y = 12$

$3 y = 2 x + 12$ $3y = 2x + 12$

$y = (\frac{2}{3}) y + 12$ $y = (2/3)y + 12$

Slope of this line is $m = \frac{2}{3}$ $m = 2/3$

$Slope of Line A m_{a} = 2$ $"Slope of Line A " m_a = 2$

$Slope of Line B m_{b} = \frac{2}{3}$ $"Slope of Line B " m_b = 2/3$

$Slope of Line C m_{c} = - (\frac{2}{3})$ $"Slope of Line C " m_c = -(2/3)$

$Slope of Line D m_{d} = - (\frac{3}{2})$ $"Slope of Line D " m_d = -(3/2)$

$since m_{d} = - \frac{1}{m}, D is perpendicular to the given line$ $"Since " m_d = - 1/ m, D " is perpendicular to the given line"$