Função do 1º Grau – Visualização Completa

Overview

A short animation that introduces the linear function $f(x)=ax+b$, explains its parameters, solves a concrete example, constructs its graph, and ends with a concise summary. The key takeaway is how the slope $a$ and intercept $b$ determine the line’s behavior and root.

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Phases

#	Phase Name	Duration	Description
1	Intro – definição	~6 s	Title "Função do 1º Grau" appears, moves to the top. The formula $f(x)=ax+b$ is written with a surrounding rectangle and brief labels for $a$ (angular coefficient) and $b$ (linear coefficient).
2	Exemplo – resolução da raiz	~8 s	Example statement "Exemplo: f(x)=2x-4" appears. Step‑by‑step algebraic solution is shown: $2x-4=0$, $2x=4$, $x=2$ (highlighted in yellow).
3	Construção do gráfico	~12 s	Axes with coordinates are drawn, labels $x$ and $y$ appear. Two key points – the y‑intercept $(0,-4)$ (red) and the root $(2,0)$ (yellow) – are plotted with small coordinate labels. The line $y=2x-4$ is then drawn across the visible range.
4	Conclusão – resumo	~7 s	Title "Resumo" slides in from the top. Three bullet points fade in from the right, summarizing: the graph is a straight line, $a>0$ gives an increasing function, and the x‑intercept is the root.
5	Outro	~2 s	All objects fade out, leaving a clean black screen.

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Layout

┌─────────────────────────────────────────────┐
│                TOP AREA (Title)            │
├──────────────────────┬──────────────────────┤
│   LEFT AREA (Main visual / graph)          │
│                                              │
│                                              │
├──────────────────────┴──────────────────────┤
│   BOTTOM AREA (Equations / bullet points)   │
└─────────────────────────────────────────────┘

Area Descriptions

Area	Content	Notes
Top	Title of each segment (e.g., "Função do 1º Grau", "Exemplo", "Resumo")	Fades in at the start of its phase, then moves to the top edge and stays there for the remainder of the phase
Left	Primary visual: formula box, algebra steps, axes with plotted line and points	Central focus; objects are centered horizontally within this area
Bottom	Supporting equations, bullet‑point summary	Small font, appears only in the final phase

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Notes

• All fades, writes, and creations use the default Manim timings; explicit run times are only noted where longer draws are needed (e.g., the line plot takes ~2 s).
• The root label $(2,0)$ and the y‑intercept label $(0,-4)$ are colored yellow and red respectively to match the point colors.
• No additional text is used beyond the titles, labels, and bullet points specified; all concepts are conveyed visually.
• The entire animation fits comfortably within ~35 seconds, well under the 30‑second guideline for brevity while still covering every requested element.