“Which equation best models the data?” looks like a statistics course crammed into one question. On Desmos it's a table plus one line containing a tilde.
The move: Type the data, fit it with ~.
Why it works: The ~ operator tells Desmos to find the parameter values that fit your data best — it does the fitting; you just name the shape (line, quadratic, exponential).
The pattern
- Enter the points as a table
- Type the model with ~ (y₁ ~ …)
- Read the fitted numbers
Worked example: The table shows x: 1, 2, 3, 4 and y: 5, 8, 11, 14. Which equation models the data?
- Build a table with the given values (the + button → table on the real thing).
- Type y₁ ~ ax₁ + b. That squiggle (~) tells Desmos: find a and b for me.
y1 ~ ax1+b - Read the parameters: a = 3, b = 2. So y = 3x + 2. Desmos did the pattern-spotting.
Worked example 2: A function passes through (0, 3), (1, 4), (2, 7), and (3, 12). Which equation models it?
- Table in.
- The y-values aren't climbing at a steady rate → not a line. Fit a QUADRATIC: y₁ ~ ax₁² + bx₁ + c.
y1 ~ ax1^2+bx1+c - a = 1, b = 0, c = 3 → y = x² + 3. The ~ fits any shape you ask for.
Remember it on test day
Tilde fits the data. That's the whole cue — say it when you see this question type and the steps follow.
When this isn't the move
If the answer choices differ in shape (linear vs exponential), check the data's pattern first — equal steps mean linear, equal ratios mean exponential.
Drill it until it's reflex
This move is one of Desvantage's 18 training modules: a plain-English lesson, a type-it-yourself walkthrough inside a live Desmos calculator, and a 100-question drill bank that deals ten fresh questions per round. The first two modules — plus the 12-question diagnostic — are free.