Check that the binomial can be translated into slope-intercept form. For a binomial to be translatable into slope-intercept form, it must contain either an x or a y term or both, and these terms may only be raised to the first power.
For example 3 + 15x, 3y + 15 and 3y + 15x are all binomials that can be translated into slope-intercept form because they contains x terms, y terms or both. On the other hand, 3 + 15x^2 cannot be translated into slope-intercept form because its x term is raised to the second power, not the first power.
Set the binomial equal to the term---x or y---that is does not contain. If the binomial contains both x and y, set it equal to 0. However, if you are explicitly told what value the binomial is equal to, such as 3x + y = 5, do not modify the equation.
For example, for the binomial 3 + 15x, set the equation equal to y because it does not contain y (y = 3 + 15x). For the binomial 3 + 15y, set the equation equal to x because the binomial doesn't contain x (x = 3 + 15y). For the binomial 3x + 15y, which contains both x and y, set the equation equal to 0 (3x + 15y = 0).
Move all y terms to the left side of the equation. To move a term from one side of the equation to the other, subtract it from both sides.
For example, move the y term in x = 3 + 15y to the left side of the equation by subtracting 15y from both sides. This yields x - 15y = 3 + 15y - 15y, which simplifies to x - 15y = 3, an equation with the y term now on the left side.
Move all x terms to the right side of the equation.
For x - 15y = 3, move the x term to the right side by subtracting x from both sides of the equation. This yields x - 15y - x = 3 - x, which simplifies to -15y = 3 - x.
Move all numbers not accompanied by an unknown variable, such as x or y, to the right side of the equation and to the right side of the x term.
For example, in -15y = 3 - x, 3 is the only number not accompanied by the unknown variables x and y. The number 3 is already on the right side of the equation, so simply move it to the right side of the x term by rearranging 3 - x to get -x + 3. This yields -15y = -x + 3.
Divide both sides of the equation by the coefficient preceding the y term. For example, in 3y, 3 is the coefficient preceding the y term. In 10y, 10 is the coefficient preceding the y term.
In -15y = -x + 3, -15 is the coefficient preceding the y term. Divide both sides of the equation by -15 to obtain (-15y) / -15 = -x/(-15) + 3/(-15), which simplifies to y = x/15 - 3/15. Re-write this as y = (1/15)x - 3/15, because x/15 = (1/15)x.
Simplify the result by reducing any fractions to their simplest form.
For example, for y = (1/15)x - 3/15, 3/15 can be reduced to 1/5, so the simplified result is y = (1/15)x - 1/5, which is also the end result in slope-intercept form.