Question

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

Answer 1

ANSWER

$- \frac{2}{3}$

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,

$y = \frac{3}{2}x + 4$

The slope of this line is

$m = \frac{3}{2}$

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.

$m \times n = - 1$

$\implies \: \frac{3}{2} n = - 1$

$\implies \: \frac{2}{3} \times \frac{3}{2}n = - 1 \times \frac{2}{3}$

$n = - \frac{2}{3}$

Therefore the slope of the new line is

$- \frac{2}{3}$