Determine the equation of the line through (-1,2) and perpendicular to the line 2x-3y+5=0

2x - 3y + 5 = 0

2x + 5 = 3y

2/3x + 5/3 = y ... slope here is 2/3. A perpendicular line will have a negative reciprocal slope. All that means is " flip " the slope and change the sign. So our perpendicular line will have a slope of - 3/2.

y = mx + b

slope (m) = - 3/2

(-1,2) ... x = - 1 and y = 2

sub and find b, the y int

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

2 = 3/2 + b

2 - 3/2 = b

4/2 - 3/2 = b

1/2 = b

so ur perpendicular equation is : y = - 3/2x + 1/2 or 3x + 2y = 1 or 3x + 2y - 1 = 0