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Chapter 6: Problem 51

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(y=m x+b\) for \(m\)

Short Answer

Expert verified
The result of the operation is \(m = (y - b)/x\). This formula still describes a straight line, but now written in terms of the slope rather than the dependent variable \(y\).

Step by step solution

01

Understand the Problem

The problem is asking for the equation \(y=mx+b\) to be rewritten such that \(m\) is by itself on one side of the equation. The formula represents a linear equation, so we are trying to isolate the slope \(m\).
02

Rearrange the Equation

Subtract \(b\) from both sides of the equation to start isolating \(m\): \[y - b = mx\]
03

Isolate m

Now divide by \(x\) to isolate \(m\): \(m = (y - b)/x\)

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