Answer:
The equation would be y = 3/2x + 3
Step-by-step explanation:
First we have to find the slope of the original line. We can do this by solving for y.
2x + 3y = 15
3y = -2x + 15
y = -2/3x + 5
Now that we have the slope of -2/3, we know the slope of the new line will be 3/2. This is because perpendicular lines have opposite and reciprocal slopes. We can use that and a point in point-slope form to find the equation.
y - y1 = m(x - x1)
y + 3 = 3/2(x + 4)
y + 3 = 3/2x + 6
y = 3/2x + 3
