I’ve been teaching and tutoring the slope intercept form of the equation of a line for 25 years. That whole time I’ve wondered, “Why is the y-intercept called b?”
Just today I discovered the answer!
We teach it backwards.
As is typical, we teach things in reverse of how we create them. The standard (or general) form of a linear function is
f(x) = ax + b
But this crazy f(x) notation isn’t really needed when you first learn to graph. We use y instead. So we have
y = ax + b
The nifty thing about this equation is that the number next to the x (in this case a) is the slope — or the measurement of how much the line tilts.
The fancy letter for the slope is m. So we change the basic equation to include the slope notation…
y = mx + b
Turns out that the b here is also exactly where the line smacks into the y-axis — AKA the y-intercept. But there’s no fancy letter for that, so we just leave it as b.
And we present that first!
We tell early students of algebra that the slope intercept form of the equation of a line is
y = mx + b
where m = slope and b = y-intercept. But we don’t bother to tell them why we’re using such crazy letters!
But now you have it. That’s the answer to the question, “Why is the y-intercept called b?”
(If only we could figure out why they called the slope m!)
Share your thoughts in the comments or on twitter/x.
