Lab: The Expression Machine
Feed the machine a value for x and watch each term grow into a bar. Substitution you can see.
Expression machine: 3x + 2
3x term
constant 2
total
3(4) + 2 = 14
Try it
Challenge: with a = 3 and b = 2, what x makes the total 20?
Drag the x slider until the gold total bar reads 20, then type x.
What to notice: the blue bar (the x term) stretches with x while the teal bar (the constant) never moves. The total is always blue + teal.
Why it works
Evaluating ax + b means scaling the x-bar by a and then stacking the constant bar. Negative values flip a bar to the left — that is all “negative substitution” ever is.