surface example

3D Plane Graph

A flat plane with constant slope.

z = 2*x - y + 1

Teacher prompt

What do the coefficients tell you?

They tell you the slope in the x and y directions.

min z 0.00max z 0.0056 samples

What this graph represents

Changing x always raises z twice as fast as changing y lowers it.

Where it appears in calculus

Use it to explain tangent planes before nonlinear examples.

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Related graphs

Open another surface page and compare shape, slices, and contour behavior.

Saddle Surface

z = x^2 - y^2

A saddle surface curves up in one direction and down in the perpendicular direction.

Gaussian Surface

z = exp(-(x^2 + y^2))

A smooth bell-shaped surface centered at the origin.

Elliptic Paraboloid

z = x^2 + y^2

A bowl-shaped surface that opens upward.

Inverted Paraboloid

z = 12 - x^2 - y^2

A dome-shaped surface with a highest point at the center.