Write an equation in slope-intercept form of the line perpendicular to y = 3x + 4 that passes through the point (3, 4). A) y = 3x - 5 B) y = 3x + 5 C) y = 1 3 x + 5 D) y = - 1 3 x + 5

Answer:The correct answer option is D. [tex]y= -\frac{1}{3} x+5[/tex].Step-by-step explanation:We are to find the equation of a line which is perpendicular to the following line and passes through the point (3, 4):[tex]y = 3x + 4[/tex]We know that an equation perpendicular to another equation has a slope which is the negative reciprocal of the first equation.So our required slope is [tex]-\frac{1}{3}[/tex]Finding the y-intercept:[tex]y=mx+c[/tex][tex]4=-\frac{1}{3}(3)+c[/tex][tex]c=5[/tex]Therefore, the equation of the line perpendicular to [tex]y = 3x + 4[/tex] and passing through the point (3, 4) is [tex]y= -\frac{1}{3} x+5[/tex].