Perfect1600

Digital SAT · Solve it in Desmos

How to Solve Matching a Table to a Rule on Desmos (Digital SAT)

Desmos confirms a rule by graphing it through the plotted points, catching an equation that fits one row but not the rest. Read the pattern by hand when the table is clearly linear and small.

Perfect1600 Content Team·Uses the same Desmos calculator that is built into the Digital SAT

Full method for matching a table to a rule

The Desmos steps

  1. 1

    Plot the points

    Enter the table's pairs as points in Desmos to see the shape.

  2. 2

    Graph a candidate

    Type an answer choice and check that its curve passes through every plotted point.

  3. 3

    Keep the fit

    The equation whose graph hits all the points is the match; wrong rules miss at least one.

Open a real question in the same Desmos calculator you get on Perfect1600, with the setup already typed in:

Worked in Desmos

Easy example
Values of the linear function f
xf(x)
0-3
10
23
The table lists f(x)f(x) for selected values of xx. Which equation could define the linear function ff?
A
f(x)=−3x+3f(x)=-3x+3
B
f(x)=3x+3f(x)=3x+3
f(x)=3x−3f(x)=3x-3
D
f(x)=x−3f(x)=x-3

A: Incorrect. ff increases, so the slope is positive.

B: Incorrect. The intercept is −3-3, not +3+3.

C: Correct. f(0)=−3f(0)=-3 gives intercept −3-3, and ff rises 3 per step, so f(x)=3x−3f(x)=3x-3.

D: Incorrect. The slope is 3, not 1.

Explanation

Intercept -3, slope 3: f(x) = 3x - 3.

Medium example
Values of the linear function f
xf(x)
0-5
23
411
The table records four values of the linear function ff. Which equation gives ff?
f(x)=4x−5f(x)=4x-5
B
f(x)=−5x+4f(x)=-5x+4
C
f(x)=4x+5f(x)=4x+5
D
f(x)=2x−5f(x)=2x-5

A: Correct. f(0)=−5f(0)=-5 gives intercept −5-5, and ff rises 8 over a run of 2, a slope of 4, so f(x)=4x−5f(x)=4x-5.

B: Incorrect. This swaps the slope and the intercept.

C: Incorrect. The intercept is −5-5, not +5+5.

D: Incorrect. The slope is 4, not 2.

Explanation

Intercept -5, slope (3-(-5))/2 = 4: f(x) = 4x - 5.

Hard example
Values of the linear function f
xf(x)
0-1
51
103
The table below gives f(x)f(x) at the indicated values of xx. Which equation could define the linear function ff?
f(x)=25x−1f(x)=\frac{2}{5}x-1
B
f(x)=52x−1f(x)=\frac{5}{2}x-1
C
f(x)=25x+1f(x)=\frac{2}{5}x+1
D
f(x)=−25x−1f(x)=-\frac{2}{5}x-1

A: Correct. f(0)=−1f(0)=-1 gives intercept −1-1, and ff rises 2 over a run of 5, a slope of 25\frac{2}{5}, so f(x)=25x−1f(x)=\frac{2}{5}x-1.

B: Incorrect. The slope is 25\frac{2}{5}, not 52\frac{5}{2}.

C: Incorrect. The intercept is −1-1, not +1+1.

D: Incorrect. ff increases, so the slope is positive.

Explanation

Intercept -1, slope (1-(-1))/5 = 2/5: f(x) = 2/5 x - 1.

Try it with the calculator

Question 1easy
Values of the linear function f
xf(x)
05
18
211
314

The table gives several values of the linear function ff. Which equation could define ff?

Question 2easy
Graph in the xy-plane
-4-202401234xy

The graph of a line in the xyxy-plane is shown. Which equation could define the line?

Question 3 is ready when you are

Keep going with more questions of this type, each with the same step-by-step reasoning. Free to start.

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Desmos questions

Can Desmos solve matching a table to a rule questions on the SAT?

Desmos confirms a rule by graphing it through the plotted points, catching an equation that fits one row but not the rest. Read the pattern by hand when the table is clearly linear and small.

Is the Desmos calculator really built into the Digital SAT?

Yes. The Bluebook testing app includes the Desmos graphing calculator on every Math question, so the method here is one you can use on test day, not a workaround.

Should I still learn the algebra?

Yes. Desmos is fastest when you know what to type and what to read. Learn the underlying method on the full guide, then use the calculator to move quickly and to check your work.

Master matching a table to a rule, calculator and all

Every Digital SAT question type comes with the method, the Desmos shortcut, and free practice with instant feedback.

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