Rearrange formulas to isolate a chosen quantity, including formulas with quadratic terms.
Rearrange a formula to isolate a chosen variable
Problem
Given \(y=mx+b\) with \(x\ne~0\), isolate \(m\). Undo the vertical intercept before dividing the full difference by \(x\).
Big Picture
What this problem is really about
The target m is multiplied by x before the constant is added, so we reverse those operations in the opposite order. We’ll subtract the intercept term first, then divide the entire remaining difference by nonzero x, preserving that difference as one grouped numerator.
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