Q:

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

Accepted Solution

A:
ANSWER[tex]- \frac{2}{3} [/tex]EXPLANATIONThe given given equation is [tex]2y - 3x = 8[/tex]We need to rewrite this equation in the slope-intercept form:[tex]y = mx + b[/tex]We add 3x to both sides.[tex]2y - 3x + 3x=8 + 3x[/tex][tex] \implies \: 2y = 3x + 8[/tex]We divide through by 2 to get,[tex]y = \frac{3}{2}x + 4[/tex]The slope of this line is [tex]m = \frac{3}{2} [/tex]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.[tex]m \times n = - 1[/tex][tex] \implies \: \frac{3}{2} n = - 1[/tex][tex]\implies \: \frac{2}{3} \times \frac{3}{2}n = - 1 \times \frac{2}{3} [/tex][tex]n = - \frac{2}{3} [/tex]Therefore the slope of the new line is [tex] - \frac{2}{3} [/tex]