What is the intercept of y+3=1/2x and y=5x-7x+8

The intercept of 2 equations is a point that verifies both equations. By that I mean that if you replace the coordinates of this point in both equations, you would get the same y.
So, to do this, you use this form of expression: y=y
So you do the equality of both expressions, and find x.
But in your case, we have one equation that is not in the y= form: y+3=1/2x.
So you subtract 3 from each side, making it y=1/2x-3
Now, we can do y=y.
1/2x-3 = 5x-7x+8
1/2x-3=-2x+8
Then, we move the variables to a side, and the numbers to the other side of the expression, so you get:
1/2x + 2x = 8 + 3
5/2x = 11
To find x, you divide both sides by 5/2:
x= 11/(5/2)
x= 11*2/5 (when you divide 2 fractions, the result is equal to the first fraction multiplied by the inverse of the second)
x=22/5

So, the intercept of y+3=1/2x and y=5x-7x+8 is 22/5.

You can check your answer (this is very important):
y+3 = 1/2 * 22/5
y+3 = 22/10
y= -8/10

y=5x-7x+8
y=5(22/5)-7(22/5)+8
y=-8/10

Hope this Helps! :)