SAT Line of Best Fit & Regression with Desmos
When the SAT gives you a table of data, Desmos can fit a line (or curve) and hand you the equation in seconds.
Step by step
- 1
Add a table
In Desmos, add a table and enter the data: x-values in the first column (x₁), y-values in the second (y₁).
- 2
Type the regression line
On a new line type: y₁ ~ a x₁ + b — using the ~ ('tilde'), NOT an equals sign. This tells Desmos to fit a line.
- 3
Read the slope and intercept
Desmos shows the best-fit values of a (the slope) and b (the y-intercept) in a results box.
- 4
Use it to predict
Plug an x into a·x + b to predict a y, or read it straight off the fitted line on the graph.
- 5
Answer the question
Slope, intercept, predicted value, or the line's equation — all come from the a and b Desmos found.
Pro tip
The ~ (tilde) is the whole trick: y₁ = a x₁ + b graphs nothing useful, but y₁ ~ a x₁ + b runs the regression. For curved data, try y₁ ~ a x₁² + b x₁ + c.
Try it yourself
Work the example right here in a live Desmos calculator — no Bluebook needed.
Data: (1, 2), (2, 5), (3, 7), (4, 10). What is the slope of the line of best fit, to the nearest tenth?
The data is in the table and the y₁ ~ a x₁ + b line is fitting it. Read a (the slope) in the results.
Loading interactive calculator…
Show the answer
Answer: 2.6
Put the points in a table as x₁, y₁, then type y₁ ~ a x₁ + b. Desmos returns a ≈ 2.6.
Put the trick to work on a real test
Full-length adaptive SAT mocks · real Bluebook-style timing · detailed score reports