Question

If the lines 6x + 5y − 7 = 0 and 2px + 5y + 1 = 0 are parallel, find the value of p.

Answer 1

For two lines a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 to be parallel, the ratio of their x and y coefficients must be equal:

`a_1/a_2 = b_1/b_2`

Coefficients from the equations:

• Line 1 (6x + 5y − 7 = 0): a₁ = 6, b₁ = 5
• Line 2 (2px + 5y + 1 = 0): a₂ = 2p, b₂ = 5

Let’s simplify and solve for p:

`6/(2p) = 5/5`

`6/(2p) = 1`

6 = 2p

∴ p = 3