Slope-intercept form gives is \(y=mx+b\) where \(m\) is the slope of the line and \(b\) is the y-intercept.
You can see that in slope-intercept form the \(y\) term is alone. In order to convert \(9x-7y=-2\) into slope intercept form, you must isolate the y term.
First we'll subtract 9x from each side.
\(-7y=-9x-2\)
Now we can divide both sides by -7.
\(y= \frac{-9x-2}{-7}\)
Now we can simplify it.
\(y= \frac{9}{7}x+ \frac{2}{7}\)