If you just want to find the roots/ x-intercept, you just have to plug in 0 for y
0=7x+8
8=7x
8/7=7x/7
8/7=x
8/7 is the root/ x-intercept/ solution
If you want to find the y intercept, just by looking at the equation you can find it. Since it's in slope intercept form, the y intercept is 8.