Slope intercept form:
y=mx+b
Where:
m= slope
b= y-intercept
We have:
m= -9/7
y= -9/7x + b
Replace (x,y) with the given point (-4,6) and solve for b
6 = -9/7(-4) +b
6 = 36/7+ b
6 - 36/7 = b
b= 6/7
y= -9/7x + 6/7
General form:
ax + by + c = 0
9/7x + y - 6/7