What is the equation of the line passing through the point (0, 8) and perpendicular to the line through the points (6, 8) and (8, 6)

Expert Answers
justaguide eNotes educator| Certified Educator

The slope of a line passing through the points `(x_1, y_1)` and `(x_2, y_2)` is S = `(y_2 - y_1)/(x_2 - x_1)` . The product of the slope of two perpendicular lines is equal to -1.

If a line passes through the points (6, 8) and (8, 6) its slope is `(6 - 8)/(8 - 6) = -1` .

The slope of a line perpendicular to this line is `(-1)/(-1)` = 1. If this line passes through the point (0, 8) the equation of the line is `(y - 8)/(x - 0) = 1`

=> y - 8 = x

=> x - y + 8 = 0

The equation of the required line is x - y + 8 = 0