Question

Answer In slope intercept form (y =Mx +b)

What is the equation of a line that is perpendicular to 2x + y = -4 and passes through the point (2, -8) thank you so much!

Answer 1

Answer: y = $\frac{x}{2}$ - 9

Step-by-step explanation:

Two lines are said to be perpendicular if the product of their slope = 1 , that is , if the slope of the first line is $m_{1}$ and the slope of the second line is  $m_{2}$ , then  $m_{1}$ = $\frac{-1}{m_{2} }$ , that is :

$m_{1}$ X  $m_{2}$ = -1

The line given is ; 2x + y = - 4

Make y the subject of the formula so that the equation will be in slope - intercept form ; y = mx + c

that is

y = -2x - 4

comparing with the equation of line y = mx + c , it shows that  $m_{1}$ = -2

Since the second line is perpendicular to this line , it means  $m_{1}$ = $\frac{-1}{m_{2} }$

That is

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

Using the formula y - $y_{1}$ = m ( x - $x_{1}$) to find the equation of the line

$y_{1}$ = -8

$x_{1}$ = 2

substituting into the equation

y - (-8) = $\frac{1}{2}$ ( x - 2)

y + 8 = $\frac{1}{2}$ ( x- 2)

2(y+8) = x - 2

2y + 16 = x - 2

2y = x - 2 - 16

2y = x - 18

y = $\frac{x}{2}$ - 18/2

y = $\frac{x}{2}$ - 9