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