9Perpendicular line equation

Find the equation of the line perpendicular to y = (1/3)x + 2 that passes through (2, 4). Write it as y = mx + b.

The perpendicular line is y = −3x + 10. Since perpendicular slopes multiply to −1, the slope 1/3 becomes −3; using point-slope form through (2,4) and solving for y gives b = 10. Check: −3(2)+10 = 4 ✓.