You don't really solve the equation. You use it. Having said that, see the Wikipedia article, which has an adequate discussion of the equation and shows it in a few forms.
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solve it
If you solve such an equation for "y", you get an equation in the slope-intercept form.
you can only solve for one in an equation so it can equal something
There is no such thing as "solving integers". You can solve an equation, which means finding all the unknowns in that equation, but you can't solve an integer.
You solve the equation.