How to use Desmos on SAT Math

Topic: Desmos on the SAT
By: SolvePlot

Enter the relationships the question gives you, then read the quantity it asks for. Graphs help with intersections, roots, and minimum values. Regression helps fit unknown parameters. Check the result against every condition before choosing an answer.

Original worked examples

The digital SAT includes Desmos inside Bluebook. Practise in Bluebook before test day so the controls feel familiar. SolvePlot is a study tool for learning these methods; it is separate from the calculator available during the exam.

A calculator can do the calculation, but you still decide what the variables mean and which result answers the question. Start with the original equation whenever possible. Rearranging it first can add work and introduce mistakes.

Which calculator method should you try?

For one equation, try graphing it exactly as written. An equation involving only $x$ can appear as a vertical line. For two equations, graph both and look for an intersection. For a quadratic, inspect its intercepts or vertex, depending on what is asked.

If a table gives values of an unknown model, regression can fit its parameters. Use the model type stated in the question, rather than picking a curve just because it seems to fit. A numerical match does not prove a statement about every possible value.

Original example

Work through the question

What value of $x$ satisfies $3x+4=19\text{?}$

Answer $x=5$

The equation 3x + 4 = 19 graphs as a vertical line at x = 5. Illustration; follow the rows below in Desmos.

What to enter in Desmos

Use one expression row for each entry. Underscores create subscripts; the tilde ~ fits parameters.

```
3x+4=19
```
Type the whole equation in one expression row. Keep the right-hand side.

Read the result

The graph is a vertical line at x = 5. Click or tap the line to inspect a coordinate; its x-coordinate is the solution. The y-coordinate can vary because y does not occur in the equation.

Check it

Substitute $5$ into the original equation: $3(5)+4=19\text{.}$ Both sides agree.

Try the entries in Desmos

The algebraic solution

Subtract $4$ from both sides to get $3x=15\text{.}$
Divide by $3$ to get $x=5\text{.}$

When is each method useful?

Use Desmos when

Graphing is useful when rearranging the equation would take several steps or when you want to check an answer. The same idea extends to equations with curves and several solutions.

Use algebra when

For this short equation, subtraction and division are likely simpler than entering a graph. Desmos is an option, not a requirement for every calculation.

Common mistakes to avoid

Enter both sides, including signs and parentheses.
Read the requested coordinate. A vertical line gives x; a horizontal line gives y.
A blank viewing window does not prove there is no solution. Adjust the axes and inspect the equation.
Keep exact values when the question needs them. A rounded decimal may hide a difference between choices.

Try one yourself

Solve $4x-7=17$

See the answer and steps

$x=6$

The equation graphs as a vertical line at $6\text{.}$ Algebra gives $4x=24\text{,}$ so $x=6\text{;}$ substitution gives $4(6)-7=17\text{.}$

Desmos entries:

4x-7=17

Calculator references

The examples above are original. These official resources explain the calculator features and test-day rules.