Question

Write an equation for the line through (-1,2) and perpendicular to
1/2x + 1/3y = 1.

Answer 1

y = (2/3)x + 8/3

Explanation:

Perpendicular lines have opposite reciprocal slope

1/2x + 1/3y = 1

change the equation into slope-intercept form

multiply both sides by 6

3x + 2y = 6

2y = -3x + 6

divide both sides by 2

y = (-3/2)x + 3

opposite reciprocal of -3/2 is 2/3

y = (2/3)x + b

to find b, plug-in (-1,2)

2 = (2/3)(-1) + b

2 = -2/3 + b

b = 2 + 2/3

b = 8/3

y = (2/3)x + 8/3