Now: Equation mode (a,b → table & graph)
Tabela e diferenças
| x | y |
|---|
Diferenças (Δx, Δy, Δy/Δx)
| Δx | Δy | Δy/Δx |
|---|
Graph
Como usar (3 passos)
- Digite a equação ou os valores de a e b acima, ou clique em um exemplo.
- Adjust start/step/rows for the table; in Table→Equation mode edit x and y directly.
- Arraste duas âncoras no gráfico para perceber a inclinação e depois copie a URL ou exporte SVG/CSV.
Todos os cálculos são executados localmente no seu navegador. Nenhum dado é enviado a servidores.
Slope & intercept at a glance
- Slope a means “when x increases by 1, y changes by a.” The difference table shows the same Δy/Δx.
- b is the y-intercept (0,b). Changing b shifts the line vertically without changing a.
- Table→Equation mode infers a and b from two points and highlights rows that do not fit.
- Graph→Equation mode builds the line from two draggable anchors; vertical lines trigger an error.
- Fractional slopes stay exact internally; switch display between fraction-first and decimal.
Perguntas frequentes
Are slope a and rate of change the same?
Yes. Slope is how much y changes when x increases by 1. We show Δx=1 and Δy=a in the difference table and slope triangle.
What does b (the intercept) mean?
It is the value of y when x=0, i.e., the point (0,b) where the line crosses the y-axis. Changing b shifts the line up or down without changing its slope.
What happens when a is negative?
The line slopes downward to the right. Δy/Δx is negative and the slope triangle shows a negative rise.
How Devo get a and b from a table?
With two points (x1,y1) and (x2,y2), a=(y2-y1)/(x2-x1) and b=y1-a·x1. In Table→Equation mode we Calcular this automatically and highlight rows that do not fit.
Why do readings from the graph have slight error?
On-screen readings are approximate because of pixels. Turning on snap keeps anchors on integer grid points to reduce error.
Is there any line that cannot be written as y=ax+b?
Vertical lines (same x for two points) cannot be written as y=ax+b. The tool shows an error if anchors form a vertical line.
Posso plot fractional slopes?
Yes. We keep a and b as exact fractions internally and let you display fractions or decimals.
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