Understanding Level Curves and Contour Maps

A 2D graph of the intersection of a surface and a plane

A line parallel to the y-axis

A 3D surface

A line parallel to the x-axis

A linear equation

A quadratic equation

A surface in 3D space

A constant function

It represents the x-axis

It is the plane that intersects the surface to form a level curve

It is the plane that intersects the surface to form a contour map

It represents the y-axis

A 3D representation of a function

A graph of a linear function

A single level curve

A set of level curves for different values of C

Set f(x, y) = -8

Set f(x, y) = 4

Set f(x, y) = 8

Set f(x, y) = 0

Subtract 4x from both sides

Multiply both sides by x

Add 4x to both sides

Divide both sides by y

y = (8 - 4x) / x

y = (8 + 4x) * x

y = (8 + 4x) / x

y = (8 - 4x) * x

A linear function

A contour map

A level curve for C = 8

A 3D surface