Question

What I the slope of a line that is perpendicular to the line 2y-3x=8

Answer 1

C) -2/3

Explanation:

2y-3x=8

2y=3x-8

Divide 2 from each number to get:

y=3/2-4

The opposite reciprocal of 3/2 is -2/3

Answer 2

`- (2)/(3)`

EXPLANATION

The given given equation is

`2y - 3x = 8`

We need to rewrite this equation in the slope-intercept form:

`y = mx + b`

We add 3x to both sides.

`2y - 3x + 3x=8 + 3x`

`\implies \: 2y = 3x + 8`

We divide through by 2 to get,

`y = (3)/(2)x + 4`

The slope of this line is

`m = (3)/(2)`

Let the slope of the line perpendicular to this line be 'n' .

Then the product of the slopes of two perpendicular lines is always negative 1.

`m * n = - 1`

`\implies \: (3)/(2) n = - 1`

`\implies \: (2)/(3) * (3)/(2)n = - 1 * (2)/(3)`

`n = - (2)/(3)`

Therefore the slope of the new line is

`- (2)/(3)`