Why Didn't I Think of This Before?

Now that we are finished with 7th grade standards, we start to take the concepts that are considered pre-algebra and stretch them into algebra.  My students have a solid understanding of slope as rate-of-change and I have been really emphasizing multiple representations.  They can handle an equation in slope-intercept form pretty well. 

I wanted to introduce them to standard form and have usually done this by giving the equation and having them graph.  In years past, I found many students really struggled with For some reason, I decided on a different approach this year.  This year I gave students the x and y intercepts and asked them if they could figure out an equation that would fit.  I introduced this equation as:

____ x + ____ y = ______

It became a puzzle and eventually kids nailed the idea that if we have the points (2, 0) and (0, 3), we can write the equation as: 3x + 2y = 6.  And after 5 or 6 examples, I gave them the points: (e, 0) and (0, f) to which they responded with: fx + ey = fe. 

Now, given the equation, can we find the x and y intercepts? 
Not a problem. 

The game play at the beginning of the lesson really opened them up to the idea which made any actual instruction I had to do much easier. 

In the end, I say it was a win.