Question

Find the equation of the line that passes through the point (7,5) and is perpendicular to the line 2x - 3y=6

Answer 1

`(7,5);\ \ \ \ 2x - 3y=6 \ \ / subtract \ 2x \ from \ each \ side \\ \\-3y = -2x + 6\ \ / divide \ each \term \ by \ (-3) \\ \\ y = \frac{2} {3}x -2\\ \\ The \ slope \ is :m _(1) = ( 2)/(3) \\ \\ If \ m_(1) \ and \ m _(2) \ are \ the \ gradients \ of \ two \ perpendicular \\ \\ lines \ we \ have \\\\\ m _(1)*m _(2) = -1`


`(2)/(3)\cdot m_(2)=-1\ \ / \cdot ((3)/(2))\\\\m_(2)=-(3)/(2)\\\\Now \ your \ equation \ of \ line \ passing \ through \ (7,5) would \ be: \\ \\ y=m_(2)x+b \\ \\5=-(3)/(2)\cdot 7 + b \\ \\ 5= -(21)/(2)+b\\ \\b=5+(21)/(2) \\ \\b= (10)/(2)+(21)/(2)\\ \\b= (31)/(2)\\\\b=15.5 \\ \\ y = -(3)/(2)x +15.5`