There must be a road perpendicular to the first road, The equation of the perpendicular road to x+3y=3 must pass through (1,-6)

Answer 1

Looking for the line perpendicular to: x+3y=3 that must pass through (1,-6).

Perpendicular slopes are negative inverses of one another, so let's first find the slope of the original line.

Convert from standard form to Slope-Intercept form...

x + 3y = 3 -------> 3y = - x + 3

y = - (1/3)x + 1, so the slope of the the perpendicular line is 3.

Substitute slope and point into y = mx + b and solve for b.

(-6) = 3(1) + b ----> b = -9

Rewrite

y = 3x - 9