Question

Write an equation in slope-intercept form for the line perpendicular to y = -2x - 2 that passes through the point (3, -2).

y = -2x + 4
y = 1/2x - 7/2
y = 1/2x - 15/2
y = -2x - 2

Answer 1

y =
`(1)/(2)` x -
`(7)/(2)`

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given the line with equation

y = - 2x - 2 ← in slope- intercept form

with slope m = - 2

given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-2)` =
`(1)/(2)` , then

y =
`(1)/(2)` x + c ← is the partial equation

to find c, substitute (3, - 2 ) for x and y in the partial equation

- 2 =
`(1)/(2)` (3) + c =
`(3)/(2)` + c ( subtract
`(3)/(2)` from both sides )

- 2 -
`(3)/(2)` = c , that is c = -
`(7)/(2)`

y =
`(1)/(2)` x -
`(7)/(2)` ← equation of perpendicular line

Answer 2

The equation of the line perpendicular to y = -2x - 2 that passes through (3, -2) is y = 1/2x - 7/2.

Step-by-step explanation:

To find the equation of a line perpendicular to y = -2x - 2 and passing through the point (3, -2), we need to determine the slope of the new line. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of the new line will be the negative reciprocal of -2, which is 1/2. Therefore, the equation of the new line in slope-intercept form will be y = 1/2x + b, where b is the y-intercept.

To find the value of b, we can substitute the coordinates of the given point into the equation:

-2 = 1/2(3) + b

-2 = 3/2 + b

b = -2 - 3/2

b = -4/2 - 3/2

b = -7/2

Therefore, the equation of the line perpendicular to y = -2x - 2 and passing through the point (3, -2) is y = 1/2x - 7/2.