Question

A line is perpendicular to the line given by the equation -8= 2y+3xWhat is theslope of the perpendicular line?

Answer 1

slope of perpendicular line =
`(2)/(3)`

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

- 8 = 2y + 3x ( subtract 3x from both sides )

- 8 - 3x = 2y ( divide through by 2 )

- 4 -
`(3)/(2)` x = y , that is

y = -
`(3)/(2)` x - 4 ← in slope- intercept form

with slope m = -
`(3)/(2)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(3)/(2) )` =
`(2)/(3)`

Answer 2

The slope of the perpendicular line is 2/3

Step-by-step explanation:

Give equation: -8 = 2y + 3x

Rewritting in the form of slope-intercept form: y = mx + c

2y + 3x = -8

2y = -3x - 8

divide both sides by 2:

2y/2 = -3x/2 - 8/2

y = -3x/2 - 4

y = -3/2 x - 4

Where m = slope = -3/2

c =intercept = -4

For a line to be perpendicualr to another line, the slope of one will be the negative reciprocal of the other one.

Slope of the 1st = -3/2

reciprocal of -3/2 = - 2/3

negative reciprocal = -(-2/3) = 2/3

The slope of the perpendicular line (slope of the second line) is 2/3