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Explore y=ax+b with synced formula, table, and graph

An interactive explorer that keeps the formula, table, and graph of y=ax+b in sync. Visualize slope triangles and difference tables, infer from tables or two points, drag anchors, share URLs, export SVG/CSV, and switch to teacher mode.

A sample is computed automatically on first load. Everything runs in your browser; nothing is sent to a server.

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Now: Equation mode (a,b → table & graph)

Current line
y=2x+1

Table & differences

xy

Differences (Δx, Δy, Δy/Δx)

ΔxΔyΔy/Δx

Graph

Graph of y=ax+b
P0: P1: Drag to move (snap optional)

How to use (3 steps)

  1. Enter the equation or a,b values above, or click a sample chip.
  2. Adjust start/step/rows for the table; in Table→Equation mode edit x and y directly.
  3. Drag two anchors on the graph to feel the slope, then copy the URL or export SVG/CSV.

All calculations run locally in your browser. No data is sent to any server.

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.

FAQ

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 do I 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 compute 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.

Can I plot fractional slopes?

Yes. We keep a and b as exact fractions internally and let you display fractions or decimals.

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