Question

Line L has equation 2x - 3y = 5.

Answer 1

Answer:

y=-$\frac{3}{2}$x-13

Step-by-step explanation:

You have to convert everything to slope intercept form before starting

2x-3y=5

3y=2x-5

y=2/3x-5/3

Then,

Since Line M is perpendicular Line M's slope will be,

-$\frac{3}{2}$x

y=-3/2x+b

Enter the given point (2,-10)

-10=-3/2(2)+b

-10=3+b

b=-10-3

b=-13

so the equation for line M is

y=-3/2x-13

Answer 2

Answer:

$y=-\frac{3}{2}x -7$

Step-by-step explanation:

Line L has the equation:

$2x-3y=5$

we need to clear for y:

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

now we have the form a general line equation

$y=mx+b$

where $m$ is the slope of the line.

so the slope of the line L is:

$m_{1}=\frac{2}{3}$

and for two lines to be parallel the following condition must be met

$m_{1}*m_{2}=-1$

where $m_{2}$ in this case is the slope of line M, substituting the value $m_{1}$ to find $m_{2}$:

$\frac{2}{3}*m_{2}=-1\\ m_{2}=\frac{-1(3)}{2}\\m_{2}=-\frac{3}{2}$

This is the slope of line M, and since we also know that it passes through the point (2, -10) where $x_{0}=2$ and $y_{0}=-10$

we use the point- slope equation and substitute known values to find the equation of the line M:

$y-y_{0}=m(x-x_{0})\\y-(-10)=-\frac{3}{2}(x-2)\\ y+10=-\frac{3}{2}x+3\\y=-\frac{3}{2}x +3-10\\y=-\frac{3}{2}x -7$

the equation of line M is:

$y=-\frac{3}{2}x -7$