The equation of the parallel line would be y = 3/2x + 10
Step-by-step explanation:
In order to find this, we first need to find the slope of the first line. We can do this by solving for y.
2x + 3y = -5
3y = -2x - 5
y = -2/3x - 5/3
Now we know the slope to be 3/2 since perpendicular lines have the opposite and reciprocal. So we can use point-slope form to find the equation of the line.
y - y1 = m(x - x1)
y - 1 = 3/2(x - -6)
y - 1 = 3/2x + 9
y = 3/2x + 10
While this doesn't match any of your options, it is correct for the given parameters.
