An equation written in slope-intercept form would have the form $${\mathtt{y}} = {\mathtt{mx}}{\mathtt{\,\small\textbf+\,}}{\mathtt{b}}$$ where y and x are variables and m and b are numbers.

An equation in standard form would be: $${\mathtt{ax}}{\mathtt{\,\small\textbf+\,}}{\mathtt{by}} = {\mathtt{c}}$$ where y and x are still variables, and a, b, and c are integers.

So now you would need to make the x and y variables on the same side of the equation, with all the constants (numbers without variables) one the other side.

Say for example you have this equation in slope-intercept form:

y = $${\frac{{\mathtt{3}}}{{\mathtt{4}}}}$$x + 2

You can subtract y from both sides to get x and y on the same side of the equation:

3/4x - y + 2 = 0

Now isolate the 2:

3/4x - y = -2

But since a,b, and c, must be integers, you would need to multiply all terms by the least common denominator of the fraction(s) in the equation. In this case, it is 4:

Standard form: 3x - 4y = -8