Worth 10 points.

which function has the greatest y-intercept?

The y intercept is the value of y when x=0, it is represented by the letter b in y=mx+b
#1: b=0
#2: b=4, when x=0, y=4
#3: you have to work out b in this one by first writing the equation in point-slope form: y+4=2(x-1), when x=0, y=-6, so b=-6
#4: from the graph you can see the line cross the y axis at (0,5), so b=5

#4 has the largest y intercept. 

The y-intercept of a function is the value when x = 0
The first choice has a y-intercept of 0.
The 2nd choice has a y-intercept of 4.
The 3rd choice has a y-intercept of -6 b = y - mx = -4 -2(1) = -6
The 4th choice has a y-intercept of 5 assuming the scale is by 1.

Therefore the 4th choice has the greatest y-intercept.