Solve by Element List Regression

Equivalent Expressions (Pt. 2) on the SAT: Desmos Walkthrough

Graph both expressions, add a slider for the unknown constant, and drag it until the two curves sit exactly on top of each other.

This lesson uses sliders and direct evaluation in Desmos: put the unknown constant on a slider or a single expression line and let the calculator find the value instead of solving algebra by hand.

Take this lesson interactively

A real SAT-style question

The expression $\frac{24}{6 x + 42}$ is equivalent to $\frac{4}{x + b}$ , where b is a constant and $x greater than 0$ . What is the value of b?

$7$

$10$

$24$

$252$

How to solve it in Desmos, step by step

The idea

The two expressions are equal for every x, so graph both and use a slider for b: slide until the two curves sit exactly on top of each other.

1
Step 1
Type these two lines. The first is the given expression, the second is the target with the unknown constant b.
Type in Desmos
$y=\frac{24}{6x+42}$ $y=\frac{4}{x+b}$
2
Step 2
Desmos asks to add a slider for b. Click the add slider button, then drag the b slider until the second curve lands exactly on top of the first curve. They match when b reads 7, so the answer is A) 7.

The answer is A.

$7$

Now you try one

Same question type, different numbers. Use the exact Desmos moves from the walkthrough above.

The expression

\dfrac{35}{5x + 40}

is equivalent to

\dfrac{7}{x + b}

, where

b

is a constant and

x > 0

. What is the value of

b

Practice this with a live Desmos calculator

The interactive version of this lesson builds the Desmos graph up step by step as you click through, with a live calculator you can type into and your progress saved.

Open the interactive lesson

More Desmos SAT lessons

Circle Geometry with Perpendicular Bisector on the SAT with Desmos System of Linear Equations (No Solution) on the SAT with Desmos Reading a Coefficient off the Graph on the SAT with Desmos No-Real-Solution Quadratic on the SAT with Desmos Finding Quadratic Coefficient on the SAT with Desmos Determining Coefficients of a Polynomial on the SAT with Desmos

The full Desmos SAT course (all 31 lessons)15 Desmos SAT tricks (quick reference)Digital SAT Math formula sheet