Skill: line-forms

Three Forms Lab

One line, three names: drag m and b and watch the point-slope, slope-intercept, and standard forms update together beside the graph.

1 Three Forms Lab

Move the sliders. All three forms describe the same line — the cards update live to prove it.

m (slope)2

b (y-intercept)1

The same line, three cards.

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Three experiments.

1. Point-slope uses (0, b)

The lab writes point-slope with the y-intercept as its point: y − b = m(x − 0). Any point works — the lab just picks the easiest.

2. Standard form clears fractions

Set m = 1.5: slope-intercept shows y = 1.5x + b but standard form shows clean integers like 3x − 2y = −4.

3. Same line, same points

Pick any x, evaluate all three cards — they always agree, because the algebra says so.