Question

What is the slope of the line 8x + 6y = 30

Answer 1

Transpose the equation:

8x+6y=30
First minus 8x from each side of the equation.
6y=30-8x
Then divide each side by 6.
y=5-1.33x   or if you want the answer in exact form:
y=5-4/3x
The slope is 4/3 or 1.333.

Answer 2

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=$\frac{-4x+15}{3}$

We can separate that fraction and we have:
$y=- \frac{4}{3}x+5$

Now that we have it in the right format we can see that if you look at the formula y=mx+b then m= $- \frac{4}{3}$ 

Hope that helps.