Slope Y-Intercept Form to Standard Form

My students are having some trouble with changing slope y-intercept form of a line to standard form and vice versa. You must first understand solving equations before this will make sense. Having a good grasp of variables on both sides of the equation will help since it involves moving a variable term from one side of the equation to the other.

Here is an example:

Rewrite y = 2x - 5 (slope y-intercept form) as standard form.

Move the 2x to the left side of the equation with the y. -2x + y = -5

That is all that is required for this one. It is now in standard form (Ax + By = C).

Another part of the assignment that we worked on required that the standard form be written with integers (no fractions).

Rewrite 3/5y = 2/3x + 2 in standard form using integers.

Move the x term to the left side of the equation. -2/3x + 3/5y = 2
Now to get rid of the fractions, you will multiply both sides of the equation by 15 (the least common multiple of 3 and 5). You could multiply by any multiple of 3 and 5 but generally we use the least common multiple. As long as this multiplication is done to BOTH sides, the equation will stay balanced. Hint: Remember that you must use the distributive property on the left side of the equation.

15[-2/3x + 3/5y] = 2(15)

-30/3x + 45/5y = 30

-10x + 9y = 30 (standard form using integers)