Using the slope-intercept form (y = mx + b), you can easily find the slope! In fact, y = mx + b, where m is the slope of the line, and b is the y-intercept. While not entirely necessary, we'll rewrite the equation in slope-intercept form for simplicity. To write the equation in slope-intercept form, all you need to do is isolate y.
1. y - 4x = 8 : write the equation down
2. y - 4x + 4x = 8 + 4x : Add 4x to each side of the equation so that the -4x on the left side of the equation cancels out.
3. y = 8 + 4x. Combine like terms
4. y = 4x + 8 : Rearrange the terms according to the slope-intercept form (y = mx + b)
Now that our equation is in slope-intercept form, we can easily identify the slope and the y-intercept. y = 4x + 8 If y = mx + b, where m is the slope, and b is the y-intercept, 4 must be the slope! As you get used to doing it, you can take a lot of the steps out, so this equation really only required one or two steps. However, I figured it'd be better to explain it in detail.