Question

Find k, if the line passing through points P (-12, -3) and Q (4, k) has slope 1/2.

Answer 1

P(x₁ ,y₁ ) = P(-12,-3), 

Q(x₂ ,y₂ ) = Q(4, k) 

Here, x₁ = -12, x₂ = 4, y₁ = -3, y₂ = k

Slope of PQ (M) = (y₂ - y₁)/(x₂ - x₁)

∴ m = (k - (-3))/(4 - (-12))

∴ m = (k + 3)/(4 + 12)

∴ m = (k + 3)/16

But, slope of line PQ (m) is 1/2 ….[Given] 

∴ 1/2 = (k + 3)/16 

∴ 16/2 = k + 3 

∴ 8 = k + 3 

∴ k = 5 The value of k is 5.