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.