Answer:
y = -3/2x + 5
Step-by-step explanation:
Step 1: find the slope
2x - 3y = 9
2x - 9 = 3y
Make y the subject of the formula by dividing both sides by 3
(2x - 9)/3 = 3y/3
( 2x - 9)/3 = y
y = 2x/3 - 9/3
y = 2x/3 - 3
m = 2x/3
Note: if two lines are perpendicular to the other, both lines are negative reciprocal of each other
m = -3/2x
Step 2 : using the point slope equation
y - y1 = m( x - x1)
( 4 , -1)
x1 = 4
y1 = -1
y -(-1) = m( x - 4)
y + 1 = -3/2( x - 4)
y + 1 = (-3x + 12)/2
y = (-3x + 12)/2 - 1
LCM = 2
y = (-3x + 12 - 2)/2
y = ( -3x + 10)/2
y = -3x/2 + 10/2
y = -3x/2 + 5
The equation of the line is
y = -3/2x + 5
