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.
10x+4y=24
To simply things, we are going to divide the whole equation by 2. So the equation is now:
5x+2y=12
We need to move the 5x to the right side so we subtract 8x from both sides
5x-5x+3y=12-5x
2y=12-5x
Now we need to get y alone so we divide by 2
[tex]y= \frac{-5x+12}{2} [/tex]
We can separate that fraction and we have:
[tex]y= -\frac{5x}{2} +6[/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{5x}{2} [/tex]
Hope that helps.
