Question

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

Options

• `5/4`

• `- 5/4`

• `- 4/5`

• `4/5`

Answer 1

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

Explanation:

For two lines to be perpendicular, the sum of the products of their x and y coefficients must be zero:

(a₁ × a₂) + (b₁ × 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

∴ `k = 4/5`