Find the value of K so that the line through the given points

Question

(1,-k) and (3k,5), m = 1/2

Answer 1

Let the points are (x₁, y₁) = (1, - k) and (x₂, y₂) = (3k, 5).

Formula for the slope of the line through the two points is  (m) = [(y₂ - y₁)/(x₂ -x₁)]

1/2 = [(5 - (- k))/(3k - 1)] = 

1/2 = (5 + k)/(3k - 1)

Cross multiplication.

1(3k - 1) = 2(5 + k)

1(3k) - 1(1) = 2(5) + 2(k)

3k - 1 = 10 + 2k

Separate the variable terms and constant terms.

3k - 2k = 10 + 1

k = 11.