Lesson 01 · 8 min

Functions & regressions

Two points do not mean ‘write point-slope.’ Type table, then Add regression — or a custom tilde like y₁ ~ a/(x₁ − b). Ugly coefficients fall out in one click.

Roughly 1 in 5 math questions can be finished with a table plus a tilde (~). Custom forms (rational, exponential, quadratic through three points) are where this move actually saves minutes.

Keystrokes

Type the word table. Enter the given points.
Click Add regression. Linear for two points, quadratic for three, exponential if the stem says so.
Custom fit when the stem names a form: y₁ ~ a/(x₁ − b), or y₁ ~ a·b^{x₁}.
No table needed if you use lists: x₁ = [4, 10], y₁ = [6, 3], then the same ~ line.
Free-response decimals: type until Desmos stops. −8/3 and −2.667 both count.

Worked example

A function of the form

f (x) = \frac{a}{x - b}

passes through

(4, 6)

and

(10, 3)

. What is the value of

a

Lists (or a table) plus the custom fit y₁ ~ a/(x₁ − b). Desmos reports a = 36, b = −2. Algebra: 6(4−b)=3(10−b) → b=−2, a=36. The algebra is why you don’t do it that way on the clock.

Answer: 36

Try it here

Loading Desmos…

Timed-test version

See points and a named form? Don’t write point-slope. Table, tilde, read the coefficient.

Pitfall

Regression is not a statistics topic on the SAT. It is a solver for the numbers that define a function. The button is linear by default — switch to quadratic/exponential, or type the custom form the question named.

Three practice questions All lessons