Hey there!
Use the slope formula.
m= (y2-y1)/(x2-x1)
Plug in the points. (-4,5) and (4,1)
m= (1-5)/(4-(-4)
m= -4/4+4
m=-4/8
m=-1/2
To find the y-intercept, first plug it into the the point slope. You just need one set of points for this, I will use (4,1)
y-y1=m(x-x1)
y-1= -1/2(x-4)
y-1=-1/2x+2
Add 1 to the other side.
y= -1/2x+3
The 3 is your y-intercept. It is in slope intercept form now. (y=mx+b) The b is the y-intercept.
The equation of the line is usually represented by the slope intercept form, which you already have: y=-1/2x+3.
I hope this helps!
~kaikers