Question

The slope of a line (6, k) and (1 − 3k, 3) is `1/2`. The value of k is ______.

Options

• −11

• 11

• `-1/11`

• `1/11`

Answer 1

The slope of a line (6, k) and (1 − 3k, 3) is `1/2`. The value of k is −11.

Explanation:

Here,

Points: (6, k) and (1 − 3k, 3)

Slope (m): `1/2`

Using the slope formula:

`m = (y_2 - y_1)/(x_2 - x_1)`

`1/2 = (3 - k)/((1 - 3k) - 6)`

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

Cross-multiply to solve for k:

1(− 3k − 5) = 2(3 − k)

−3k − 5 = 6 − 2k

−3k + 2k = 6 + 5

−k = 11

∴ k = −11