"how to use a linear function to estimate basic financial costs from a baseline and a per-unit cost"

If you told me what those words meant, I could probably figure it out ;-)

Ok! This should be easy.

"Linear function": f(x) = mx+b, or y=mx+b. You know, from 8th-grade algebra.

"Baseline and per-unit cost". So your "baseline" cost is how much you have to pay before you get the first unit of your item. Like, if your buying, say, chocolates, the "baseline" is the cost of the box, with no chocolates in it, or of shipping-and-handling. Then the per-unit costs is just how much you pay for each chocolate.

We then map those onto the math:

"Baseline" -- that's the y-intercept, or "b".

"Per-unit cost" -- that's the multiplier for the number of units, or "m".

And voila, we've got y=mx+b: a simple formula for how much your Christmas chocolates are going to cost you.

Yup, way easier than expected. Except now they are New Years chocolates. ;-) Thanks for the reply!

> we can do a bunch more with the non-gifted children than we even attempt.

We can. But it requires a lot more teachers. And nobody is willing to pay for that.

The public education system in the US is at a rough optimum relative to the amount of parental resources that people are willing to spend. If you want to overcome that, then you need to spend a dramatic amount more on teachers and schools (the Gates Foundation data is quite clear on this--25% expenditure increase only begets about 1-3% student achievement increase--you need nearer to 100% increases to get significant levels of student improvement).

I'm in mensa, and "use a linear function to estimate basic financial costs from a baseline and a per-unit cost" is still foreign to me. I could probably get the outcome you're trying to get at, but those words don't do anything for me but put me on edge.

In English: If a widget factory costs F and makes a widget for W dollars, how much will it cost to build N widgets? If you have a budget of B dollars and you need to build N widgets, how much can your process cost per widget? If your budget is B and your widgets cost W, how many can you build?

  y = mx + b
  ("basic financial costs") = ("per unit cost")x + ("baseline")

Makes so much more sense, and I can think about that in software quite easily. I've been working professionally in software for 20 years, and programming as a hobby for about 13 years before that. As a kid, I got in to programming early on, but never really grokked 'math' as a formal thing, and while I know I can do a lot of 'math stuff', I don't know the lingo very well above algebra stuff.

It's a bit hard "confessing" that sort of stuff in a forum like this amongst loads of people who likely are all demonstrably smarter than me in multiple disciplines, and many of whom are self-taught as well. I feel like I should have a 'kick me' sign on me at times - perhaps this is the famed "impostor syndrome"?

It wasn't very good phrasing, but it's genuinely hard to phrase these things when you can't just say, "y=mx+b". This then has the problem that I've actually heard of a case in which a professional working at a nonprofit with other professionals said "y=mx+b" and received blank stares.

Thanks.

FWIW, I wrote "I'm in mensa" not to brag so much as ... I got in through test scores, and (obviously) have some raw measure of ability in cognitive areas, but still wasn't able to immediately get that algorithm from the english. I get what it means, and understand the implications of the algorithm, but couldn't make that immediate jump. The older I get, the harder it is for me to tell when someone is sharp and maybe just can't grasp something immediately, and when they truly can't get it. I probably make more allowances than I did in my youth, precisely because I know my own shortcomings more now than 20 years ago.