The Best Way to Write Linear Equations in Standard Form

Mathematicians love mathematically-sound shortcuts. Part of what draws people to mathematics is an ability to recognize patterns and use efficient procedures. I frequently look for these kinds of strategies to help make mathematics more accessible for students.

In Algebra 1, students spend a great deal of time writing linear equations. Given a point and the slope, they practice writing equations in slope-intercept, point-slope, and standard form. Not surprisingly, standard form tends to cause the most frustration and often results in lower quiz scores.

Fortunately, there is a strategy that helps. The approach below uses proportions to simplify the process and make writing equations in standard form more accessible.

Example:

Step 1: Use point-slope form (rearranged).

Solve point-slope form for m. Hint: This looks a lot like the slope formula!  Substitute m, x₁, y₁ into the equation.

Step 2: Cross-multiply.

Treat the equation as a proportion and set the cross products equal to each other.

Step 3: Distribute.

Use the Distributive Property to eliminate the parentheses.

Step 4: Rearrange to Ax+By=C.

Use addition and subtraction to rearrange the terms to standard form. Notice there are no frustrating fractions to clear!

Click here to learn more about resources that aid in teaching students how to write linear equations.