Help with more algebra

write an equation in slope-intercept form for the line that has a slope of -3/2 and passes through (-4,1)

slope intercept formula:
y - y1 = m (x - x1)

m = -3/2
(x1, y1) = (-4,1)
y - 1 = -3/2 (x + 4)
y = -3/2x + -6 + 1 = -3/2 x -5

so y = mx + c

m=slope=-3/2

so y = -3/2x + c

sub in point

1 = (-3/2)*(-4) + c

1 = 6 + c

c=-5


so y = -3x/2 - 5

sub. into y - y1 = m(x-x1)
y - 1 = -3/2( x - -4)
y -1 = -3/2 x +6
y = -3/2 x +7

y-1 = -3/2 (x + 4)

y-1 = -3/2x -6
y=-3/2x-5