The form for the y-intercept equation is y=mx+b where m=the slope. If we can get it into that format, it will give us the slope. So we need to solve for y.
8x+6y=30
To simply things, we are going to divide the whole equation by 2. So the equation is now:
4x+3y=15
We need to move the 4x to the right side so we subtract 8x from both sides
4x-4x+3y=15-4x
3y=15-4x
Now we need to get y alone so we divide by 3
3y/3=[tex] \frac{-4x+15}{3} [/tex]
We can separate that fraction and we have:
[tex]y=- \frac{4}{3}x+5[/tex]
Now that we have it in the right format we can see that if you look at the formula y=mx+b then m= [tex]- \frac{4}{3} [/tex]
Hope that helps.
