GOZUNTA
Try it now
All courses Algebra I · A-CED.4 50 of 76
Rearrange formulas to isolate a chosen quantity, including formulas with quadratic terms.

Rearrange a formula to solve for a chosen variable

Problem
Rearrange \(y=mx+b\) to solve for \(x\), with \(m\ne~0\). Track how subtracting the constant term and dividing the entire remaining expression isolates \(x\).
Your answer
Show answer choicesHide answer choices Work through the mathematics first, then compare your reasoning.Select the answer that matches your work.
With a free account

Choose exactly what to practice.

Browse the learning objectives and included problem types, then build a session around the math you want to work on.

Create a free account
With paid access

Connect the whole math pathway.

All-course access opens Math Foundations and Math I–III, from prerequisite review through advanced work.

Compare plans

Hint

Undo the \(+b\) first so the term with \(x\) is by itself. Start from \(y=mx+b\) and subtract \(b\) from both sides.

To solve for \(x\), isolate the term \(mx\) first, then divide both sides by \(m\). Dividing by \(m\) requires \(m\ne 0\).

Solution walkthrough

01

State the goal and restriction

\[y=mx+b;~\text{solve}~\text{for}~x;~m\ne~0\]

The variable x is multiplied by m and then b is added. The restriction m!=0 is required because isolating x will divide by m.

02

Undo the added constant

\[\begin{aligned} y-b=mx+b-b \\ y-b=mx \end{aligned}\]

Subtract b from both sides to preserve equality and remove the constant from the side containing x.

03

Undo multiplication by m

\[\begin{aligned} (y-b)/m=mx/m \\ (y-b)/m=x \end{aligned}\]

Divide both sides by nonzero m. The entire difference y-b must remain grouped in the numerator.

04

Write and verify the rearrangement

\[\begin{aligned} x=(y-b)/m \\ m((y-b)/m)+b=y-b+b=y \end{aligned}\]

The formula solved for x is x=(y-b)/m. Substituting it into the original right side simplifies back to y, confirming equivalence when m!=0.

+

Another way

  1. Treat mx=y-b as a single multiplication equation and apply the inverse operation division by m to both sides.

!

Common mistake

Do not divide only b by m or write y/m+b. Subtract b first, then divide the entire remaining difference y-b by m.

Solution walkthrough video