write the equation of the line through (1,-5) and perpendicular to -3x+2y=12

Answer 1

-3x + 2y = 12

2y = 3x + 12

y = (3/2)x + 12

Perpendicular lines have opposite, reciprocal slopes, so our new line will have a slope of -2/3. We can solve 2 ways...

y - y₁ = m(x - x₁)

y - (-5) = (-2/3)(x - 1)

y + 5 = (-2/3)x + 2/3

y = (-2/3)y - 4 1/3

y= mx + b

-5 = (-2/3)(1) + b

-5 = -2/3 + b

b = -4 1/3

y = (-2/3)x - 4 1/3