If the lines 4x + 5y = 7 and x − ky + 1 = 0 are perpendicular, then the value of k is ______.

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If the lines 4x + 5y = 7 and x − ky + 1 = 0 are perpendicular, then the value of k is ulbb($\frac{4}{5}$). Explanation: For two lines to be perpendicular, the sum of the products of their x and y coefficients must be zero: (a1 $\times$ a2) + (b1 $\times$ b2) = 0 Using the given equations: Line 1 (4x + 5y = 7): x is 4, y is 5, Line 2 (x − ky + 1 = 0): x is 1, y is −k, Putting values in the formula, 4(1) + 5(−k) = 0 4 − 5k = 0 5k = 4 $\therefore$ k = $\frac{4}{5}$

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