Answer:
G. [tex] y = \frac{1}{2} x + 1[/tex]
Step-by-step explanation:
[tex] \because \: line \: m \: is \: passing \: through \: the \: \\ points \: (3, \: 2) \: and \: (4, \: 0) \\ \\ slope \: of \: line \: m = \frac{0 - 2}{4 - 3} = \frac{ - 2}{1} = - 2 \\ \\ \because \: line \: l \perp \: line \: m \\ \\ \therefore \: slope \: of \: line \: l = - \frac{ 1}{slope \: of \: line \: m} \\ \\ \therefore \: slope \: of \: line \: l = \frac{1}{2} \\ \\ line \: l \: is \: passing \: through \: (6, \: 4) \\ \\ \therefore \:equation \: of \: line \: l \: in \: point \: slope \: \\ form \: is \: given \: as \\ \\ y - 4 = \frac{1}{2} (x - 6) \\ \\ y - 4= \frac{1}{2} x - 3 \\ \\ y = \frac{1}{2} x - 3 + 4 \\ \\ \huge \red{ \boxed{y = \frac{1}{2} x + 1}}[/tex]
