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 =
`(x)/(2)` - 9

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)` =
`(-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)` =
`(-1)/(m_(2) )`

That is

`m_(2)` =
`(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) =
`(1)/(2)` ( x - 2)

y + 8 =
`(1)/(2)` ( x- 2)

2(y+8) = x - 2

2y + 16 = x - 2

2y = x - 2 - 16

2y = x - 18

y =
`(x)/(2)` - 18/2

y =
`(x)/(2)` - 9