Question

Line L has equation 2x - 3y = 5. Line M passes through the point (2, -10) and is perpendicular to line L. Determine the equation for line M.

A) 2x + 3y = -14 B) 2x - 3y = -26 C)3x + 2y = -14 D) 3x - 2y = -26

Answer 1

C has to be the right one

Answer 2

Answer:

Option C is correct.

Step-by-step explanation:

Given Equation of Line L is 2x - 3y = 5

Line M is perpendicular to line L and Line M passes through point ( 2 , -10 )

first rewrite equation of line L in slope intercept form to get slope of line L,

$2x-3y=5$

$3y=2x-5$

$y=\frac{2}{3}x-\frac{5}{3}$

By comparing with , y = mx + c

Slope of line L = $\frac{2}{3}$

let slope of M = m1

We know that Product of slope of perpendicular lines equal to -1

So, m × m1 = -1

$\frac{2}{3}\times m1=-1$

$m1=-1\times\frac{3}{2}$

$m1=\frac{-3}{2}$

Now we find Equation of Line M using slope and point form,

$y-y_1=m(x-x_1)$

$y-(-10)=\frac{-3}{2}(x-2)$

$y+10=\frac{-3x+6}{2}$

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

$3x+2y+14=0$

$3x+2y=-14$

Therefore, Option C is correct.