Subjects algebra

Equation Rearrangement

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1. The problem asks to express the first answer in the form of the equation $py - m(x - a) = b$. 2. To do this, identify the variables and constants in the original answer and rearrange them to match the structure $py - m(x - a) = b$. 3. Suppose the first answer was $y = mx + c$ (a common linear form). 4. Multiply both sides by $p$ to get $py = pmx + pc$. 5. Rewrite $pmx$ as $m(px)$ and express $px$ as $p(x - a + a) = p(x - a) + pa$. 6. Substitute back: $py = m(p(x - a) + pa) + pc = m p (x - a) + m p a + p c$. 7. Rearranging terms: $py - m p (x - a) = m p a + p c$. 8. Let $m' = m p$, $b = m p a + p c$, then the equation becomes $py - m'(x - a) = b$. 9. This matches the desired form $py - m(x - a) = b$ with $m = m'$ and $b$ as defined. Final answer: The equation in the form $py - m(x - a) = b$ is $$py - m(x - a) = b$$ where $m$ and $b$ are constants derived from the original equation.