Point–Slope → Slope–Intercept
Algebra, Lines
Intro: Plug in m, x1, y1 and we’ll simplify to y = mx + b.
Worked example
- $y − 5 = \tfrac{3}{4}(x + 2)$
- Start from point–slope form: $$y - y_1 = m\,(x - x_1).$$ Here, $m=\tfrac{3}{4}$, $x_1=-2$, $y_1=5$, so $$y - 5 = \tfrac{3}{4}\,(x - (-2)) = \tfrac{3}{4}(x + 2).$$
- Distribute $\tfrac{3}{4}$ across the parentheses: $$y - 5 = \tfrac{3}{4}x + \tfrac{3}{4}\cdot 2 = \tfrac{3}{4}x + \tfrac{3}{2}.$$
- Add $5$ to both sides to isolate $y$: $$y = \tfrac{3}{4}x + \tfrac{3}{2} + 5.$$
- Combine constants: write $5$ as $\tfrac{10}{2}$, so $$\tfrac{3}{2} + 5 = \tfrac{3}{2} + \tfrac{10}{2} = \tfrac{13}{2}.$$ Thus $$y = \tfrac{3}{4}x + \tfrac{13}{2}.$$
- Final slope–intercept form: $$\boxed{y = \tfrac{3}{4}x + \tfrac{13}{2}}.$$
- Optional check (substitute the original point): for $x=-2$, $$y=\tfrac{3}{4}(-2)+\tfrac{13}{2}= -\tfrac{3}{2}+\tfrac{13}{2}=\tfrac{10}{2}=5,$$ which matches $y_1=5$ ✔️.
FAQs
Can x1,y1 be decimals?
Yes, decimals or fractions are fine.
Why choose Mathix?
- Get clear, step-by-step solutions that explain the “why,” not just the answer.
- See the rules used at each step (power, product, quotient, chain, and more).
- Optional animated walk-throughs to make tricky ideas click faster.
- Clean LaTeX rendering for notes, homework, and study guides.
How this calculator works
- Type or paste your function (LaTeX like
\sin,\lnworks too). - Press Generate a practice question button to generate the derivative and the full reasoning.
- Review each step to understand which rule was applied and why.
- Practice with similar problems to lock in the method.