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