To do this we need to put the equation in the standard form.
This the the standard form :
y = mx + c
Where m = slope and c = y-intercept
So now we need to rearrange your equation:
0.5y - 3x = 6 + x
To start we can add 3x to both sides of the equation:
0.5y - 3x + 3x = 6 + x + 3x
0.5y = 6 + 4x
Now we can divide both sides of the equation by 0.5:
(0.5y)/0.5 = 6/0.5 + (4x)/0.5
y = 8x + 12 ⇒ This is in the standard form now.
So now we can see, since the standard form of the equation is:
y = mx + c
We can see that for your equation:
m = 8 and c = 12
So the slope = 8 and the y-intercept = 12