Alright so first you'll want to simplify into y=mx+b format. So you'll have to get the y on it's own side.
4y=7x+1
Divide by 4 on both sides.
Y=(7/4)x+(1/4)
So your y intercept is equal to one forth or .25
Now substitute y for zero and solve for x.
(7/4)x+(1/4)=0
7x/4 = -1/4
7x=-1
Xint= -1/7
Yint= 1/4
Hope this helped!