Question type

Regression on the SAT: let Desmos find the equation

When a question gives a table of values, or exactly the points that fix a model, and asks for the equation, a coefficient or a value, use Desmos regression: make a table, then type y1 ~ mx1 + b (linear), y1 ~ ax1^2 + bx1 + c (quadratic) or y1 ~ ab^x1 (exponential). The SAT only tests these three.

These questions give data as a table, or as two or three points, and ask for the function that fits it, one of its coefficients, or a value such as $f (0)$ .

It appeared on four of the five official practice tests we analysed. It is the clearest case of a Desmos technique the exam expects you to know: by hand it is several steps, in Desmos it is one line.

On 4 of 5 official practice tests
Desmos helps

Why students miss it

Solving by hand when the calculator does it in one line, and making an arithmetic slip on the way.

Using the wrong model. The question or the choices always say which kind, linear, quadratic or exponential; regress with that one.

Rounding too early. Desmos shows several decimals; match them to the choices before rounding.

How to spot it

A table of $x$ and $f (x)$ , or two or three given points.
"Which equation defines $f$ ", or a question about $f (0)$ , the slope or a coefficient.
The model named in the question: "the linear function", "exponential".

The method

Regression in Desmos

Add a table (the + menu, then table) and type the x values in x1 and the outputs in y1.

Linear: type y1 ~ mx1 + b.
Quadratic: type y1 ~ ax1^2 + bx1 + c.
Exponential: type y1 ~ ab^x1.
Then: read the coefficients, or evaluate the model at the x you need.

With Desmos

This question type exists because of Desmos: the regression line is the intended route.

Open a table and enter the data: x1 = 2, 5, 8 and y1 = 17, 8, −1.
On a new line type y1~mx1+b. Desmos shows m = −3 and b = 23.
Read what the question asks for: here $f (0) = b = 23$ .

The ~ is the tilde key, not an equals sign. With an equals sign Desmos tries to graph an equation and fits nothing.

Two real questions

From the 1500prep bank, the way the app shows them. Answer first, then open the explanation.

1Question 1 of 2#264Alg

For a linear function $f$ , the table gives three values of $x$ and their corresponding values of $f (x)$ . $x f (x) 21758 8 - 1$ What is the value of $f (0)$ ?

Pick an answer, then check it.

Show the answer and explanation

Each 3-unit increase in

x

drops

f (x)

by 9, so the slope is

- 3

. Going back 2 units from

x = 2

x = 0

adds

2 (3) = 6

f (0) = 17 + 6 = 23

2Question 2 of 2#252Alg

A tank is drained at a constant rate. The linear function V gives the volume of water, in gallons, in the tank t minutes after draining begins. If V(6)=4200 and V(15)=2850, what is the volume of water, in gallons, in the tank when draining begins?

Pick an answer, then check it.

Show the answer and explanation

Get the rate:

\frac{2850 - 4200}{15 - 6} = \frac{- 1350}{9} = - 150

gallons per minute. To go back from

t = 6

t = 0

, add

6 \cdot 150 = 900

V (0) = 4200 + 900 = 5100

Questions students ask

How do you do regression on Desmos for the SAT?

Create a table with x1 and y1, enter the data, then type y1~mx1+b for a line, y1~ax1^2+bx1+c for a quadratic, or y1~ab^x1 for an exponential. Desmos shows the coefficients.

Which regressions are on the SAT?

Linear, quadratic and exponential only. The question or the answer choices always tell you which one to use.

Is regression the same as line of best fit?

Related, but the SAT treats them differently. Regression gives you the data and asks for the equation; line of best fit gives you the line on a scatterplot and asks you to use or interpret it.

Practise this type until it is automatic

Five more regression questions, checked instantly, with every wrong choice explained. Free, no card.

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