find the equation of the line which satisfy the given condition: The perpendicular from the origin to a line meets it at the point (–2, 9), find the equation of the line.

 Given:

Points are origin (0, 0) and (-2, 9).

We know that slope, m = (y₂ – y₁)/(x₂ – x₁)

= (9 – 0)/(-2-0)

= -9/2

We realize that two non-vertical lines are opposite to one another if and provided that their slants are negative reciprocals of one another.

m = (-1/m) = -1/(-9/2) = 2/9

We know that the point (x, y) lies on the line with slope m through the fixed point (x₀, y₀), if and only if, its coordinates satisfy the equation y – y₀ = m (x – x₀)

y – 9 = (2/9) (x – (-2))

9(y – 9) = 2(x + 2)

9y – 81 = 2x + 4

2x + 4 – 9y + 81 = 0

2x – 9y + 85 = 0

∴ The equation of line is 2x – 9y + 85 = 0.