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Digital SAT · Solve it in Desmos

How to Solve Linear Word Problems on Desmos (Digital SAT)

After the equation is written, Desmos confirms it by checking that its line passes through the given points, and it makes eliminating choices quick. The reading, turning words into a rate and a start, comes first and is yours.

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

Full method for linear word problems

The Desmos steps

  1. 1

    Graph your equation

    Type the equation you built as y = ... to see its line.

  2. 2

    Pass it through a known point

    Confirm the line hits a point the problem gives, like the cost at a stated number of units.

  3. 3

    Eliminate the rest

    Graph each candidate and keep the line that fits the starting value and the data point.

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

Worked in Desmos

Easy example

A candle is 1818 centimeters tall and burns down at a constant rate of 22 centimeters per hour. The candle has been burning for xx hours.

Which equation gives the height yy, in centimeters, of the candle after xx hours?
y=−2x+18y = -2x + 18
B
y=2x+18y = 2x + 18
C
y=18x−2y = 18x - 2
D
y=−18x+2y = -18x + 2

A: Correct. The candle starts at 18 cm and loses 2 cm each hour, so y=−2x+18y = -2x + 18.

B: Incorrect. This adds height each hour, but the candle burns down, so the rate is negative.

C: Incorrect. This swaps the starting height and the rate; 18 is the starting height, not the rate.

D: Incorrect. This swaps the values and uses the wrong sign on the starting height.

Explanation

The starting height 18 is the constant and the burn rate is −2-2 per hour, giving y=−2x+18y = -2x + 18.

Medium example
A gym charges a one-time joining fee of 30 dollars and a monthly fee of 22 dollars. Which equation gives the total amount paid TT, in dollars, after mm months?
T=30+22mT=30+22m
B
T=22+30mT=22+30m
C
T=52mT=52m
D
T=30−22mT=30-22m

A: Correct. The joining fee 30 is the constant and 22 is the monthly rate, so T=30+22mT=30+22m.

B: Incorrect. This swaps the joining fee and the monthly fee.

C: Incorrect. This drops the one-time joining fee.

D: Incorrect. Monthly fees add to the total, so the rate should be positive.

Explanation

Joining fee 30 plus 22 per month gives T = 30 + 22m.

Hard example
The cost of a catering order increases linearly with the number of units. Four units cost 90 dollars and nine units cost 140 dollars. Which equation gives the cost CC, in dollars, for nn units?
A
C=10+50nC=10+50n
B
C=90+10nC=90+10n
C
C=50+15nC=50+15n
C=50+10nC=50+10n

A: Incorrect. This swaps the intercept and the rate.

B: Incorrect. 90 is the cost at 4 units, not the intercept at 0 units.

C: Incorrect. The rate is 10, not 15.

D: Correct. The rate is (140−90)/(9−4)=10(140-90)/(9-4)=10; the intercept is 90−10(4)=5090-10(4)=50, so C=50+10nC=50+10n.

Explanation

Rate 10, intercept 50: C = 50 + 10n.

Try it with the calculator

Question 1easy
Candy bars
24681010203040TimeCandy bars

The graph shows the number of candy bars a machine has wrapped after a given number of seconds. At what rate does the quantity change each second?

Question 2medium
Liters
246810102030405060TimeLiters

The line in the graph represents the number of liters of water in a draining tank after a given number of minutes. By how many units does the quantity change per minute?

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 linear word problems questions on the SAT?

After the equation is written, Desmos confirms it by checking that its line passes through the given points, and it makes eliminating choices quick. The reading, turning words into a rate and a start, comes first and is yours.

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 linear word problems, 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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