If the line joining the two points (5, 4) and (-3, k) is parallel to the line kx – y + 11 = 0, then what is the value of ‘k’?

Question

Question

Answer 1

Given:

The line joining the two points (5, 4) and (-3, k) is parallel to the line kx – y + 11 = 0

Calculation:

Equation of line joining two points:

\(\left( {y - 4} \right) = \frac{{\left( {k - 4} \right)}}{{ - 3 - 5}} \times \left( {x - 5} \right)\)

Slope of above line = \(m_1 = \frac{{4 - k}}{8}\)

Another line:

kx – y + 11 = 0

y = kx + 11

Slope of above line = k

Both the lines are parallel:

m₁ = m₂

⇒ (4 – k)/8 = k

⇒ 4 – k = 8k

⇒ 4 = 9k

⇒ k = 4/9