Equation of line p:
[tex]{\sf{2x - 3y = 4}}[/tex]
[tex]{\sf{y = \frac{2x}{3} - \frac{4}{3}}}[/tex]
Slope of line p (m):
[tex]{\sf{\frac{2}{3}}} [/tex]
Since, l is perpendicular to line p, the product of slopes of line l & p should be -1. We assume slope of line l be m2
Hence,
[tex]{\sf{m \times m2 = - 1}}[/tex]
[tex]{\sf{ \frac{2}{3} \times m2 = - 1}}[/tex]
[tex]{\sf{m2 = \frac{ - 3}{2}}}[/tex]
Since, line l passes through points (6, 0).
We apply,
[tex]{\sf{(y - y1) = m2(x - x1)}}[/tex]
[tex]{\sf{y - 0 = \frac{ - 3}{2}(x - 6)}} [/tex]
[tex]{\sf{2y - 0 = - 3x + 18}}[/tex]
[tex]{\sf{3x + 2y - 18 = 0}}[/tex]
The equation of line l:
[tex]{\sf{\red{\boxed{\sf{3x+2y-18=0}}}}}[/tex]
