Hello there!
Since the equation you gave is in slope-intercept form, we can simply find the y-intercept by only looking at the equation.
slope-intercept form is:
y = mx + b
m : slope
b : y-intercept
Your equation is y = 8x + 7
y = mx + b
y = 8x + 7
So the y-intercept is 7.
Hope this helped!! :)