Question: Will the point go through the line?
Students made their guesses and we split the room into the two camps: Yes and No.
Cheaters were cast out!
Alright, I didn't really cast him out. But we did have a short conversation
on how reliable the paper would be in determining whether or not the point is on the line.
We need more information:
Not quite enough to determine slope intercept form, but enough to get a fairly good guess as to the slope of the line. Students wrote their guesses for the equation and all groups came up with:
y = -3/4 x + 4
Are you sure about this equation?
Nah, we need a bit more information.
Now we have both intercepts; enough to verify our slope and enough to write the equation in Standard Form.
But, do we have enough info to determine whether or not the point is on the line?
So we verified two different ways:
Continuing with the pattern determined by the slope.
Plugging the point into both equations to see if they are satisfied.
The coolest part about this is that a colleague and I developed this lesson in about 10 minutes. It's pretty rewarding when minds get together and focus on interesting ways to deliver instruction centered around a simple question. Have to give credit to Dan for stoking the fire.