Statement-I if two lines are perpendicular then their product of slopes = $- 1$
Statement-II If the straight line, $2 x - 3 y + 17 = 0$ is perpendicular to the line passing through the points (7, 17) and $(15, β),$ then $β = 5$

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Only S-I true

both are false

both S-I, S–II are correct and S-I, is correct explanation of S–II

only S-II true

answer is C.

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Detailed Solution

Given,:

$\begin{array}{l} 2 x - 3 y + 17 = 0....1 \\ T h e l i n e p e r p e n d i c u l a r t o 1 i s 3 x + 2 y = λ \\ (7, 17) \Rightarrow 3 (7) + 2 (17) = λ \Rightarrow λ = 55 \\ N o w, (7, 17) \Rightarrow 3 (7) + 2 (17) = λ \Rightarrow λ = 55 \\ (15, β) \Rightarrow 3 (15) + 2 β = 55 \Rightarrow β = 5 \end{array}$