The straight lines 3x − 5y = 7 and 4x + ay + 9 = 0 are perpendicular to one another. The value of a is ______.

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The straight lines 3x − 5y = 7 and 4x + ay + 9 = 0 are perpendicular to one another. The value of a is ulbb($\frac{12}{5}$). Explanation: For two lines a1x + b1y = c1 = and a2x + b2y = c2 to be perpendicular, the product of their x coefficients plus the product of their y coefficients must be zero: (a1 $\times$ a2) + (b1 $\times$ b2) = 0 Identify coefficients: $\Rightarrow$ Line 1 (3x − 5y = 7): a1 = 3, b1 = −5 $\Rightarrow$ Line 2 (4x + ay + 9 = 0): a2 = 4, b2 = a Plug into formula: 3(4) + (−5)(a) = 0 12 − 5a = 0 5a = 12 $\therefore$ a = $\frac{12}{5}$

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