Slope-intercept form is #y = mx + b#.
So how do we write #8x + 9y = 1# in this form? Well, we need to isolate #y# on one side and get everything else on the other side!
1. Our first step is to subtract #8x# from both sides, so that only #9y# remains on the left side.
#8x + 9y = 1#
#cancel(8x) + 9y cancel(color(red)(- 8x)) = 1 color(red)(- 8x)#
#9y = 1 - 8x#
We can switch the order of the #1# and the #-8x#, because of the commutative property. So now we have
#9y = -8x + 1#
2. Divide both sides by #9# to get only #y# on the left side.
#(9y)/9 = (-8x)/9 + 1/9#
#y = -8/9x + 1/9#
Now the equation is in slope-intercept form!
The slope (m) is #-8/9# and the y-intercept (b) is #1/9#.
