1Cademy - Solving $$m = \frac{y-2}{x-3}$$ for $$y$$

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Solving a Rational Equation for a Specific Variable

Example

Solving $m = \frac{y-2}{x-3}$ for $y$

To solve the slope-derived formula $m = \frac{y-2}{x-3}$ for $y$ , follow these steps: 1. Note restriction: $x eq 3$ . 2. Clear fractions: Multiply both sides by the LCD $(x-3)$ to obtain $m(x-3) = y-2$ . 3. Simplify: Expand to $mx - 3m = y - 2$ . 4. Isolate $y$ : Add $2$ to both sides, resulting in $y = mx - 3m + 2$ . This demonstrates how to manipulate rational equations derived from geometric formulas.