Slope-intercept form is the form:
y = mx + b

where y and x are the coordinates, m is the slope, and b being the y-intercept.

We know the formula, so we just have to rearrange into slope-intercept form.

We want y on one side like the original form has it…

10x – 7y = -8 (add 7y to both sides)

10x = -8 + 7y (add 8 to both sides)

10x + 8 = 7y

We got y in one side, but we want it simplified. We don’t want a number in front of y, so we will divide y by 7 to get rid of it.

What is done in side is done to the other.

10x + 8 = 7y

(10x + 8) ÷ 7 = y

That is it. There is nothing more that can simplify the slope-intercept equation. Good luck!