What line is perpendicular to y=3/4x-3A/ y=-4/3x+12 b/ Y=4/3+12C/ y=-3/4x+12 d/ y=3/4x+12

Accepted Solution

Option AThe line [tex]y = \frac{-4}{3}x + 12[/tex] is perpendicular to [tex]y = \frac{3}{4}x - 3[/tex]Solution:Given that line is [tex]y = \frac{3}{4}x - 3[/tex]We have to find the line perpendicular to this line.The given line equation is in form of slope-intercept formThe slope-intercept form is given as:y = mx + cWhere "m" is the slope of the line and "c" is the y-interceptOn comparing the given equation with slope-intercept form, we get[tex]m = \frac{3}{4}[/tex]If a line is perpendicular to another line, then the product of their slopes will always be -1Let the slope of line which is perpendicular to given line be "a"Then we get,[tex]\frac{3}{4} \times a = -1[/tex][tex]a = \frac{-4}{3}[/tex]Now look at the options and compare with slope intercept form and find out which option has the slope "m" = [tex]\frac{-4}{3}[/tex]Option A [tex]y = \frac{-4}{3}x + 12[/tex] has the slope [tex]\frac{-4}{3}[/tex]Thus option A is correct