Understanding Intercepts and Traces in 3D Space

What is an intercept in 3D space?

• A point where a graph intersects a line

• A point where a graph intersects a curve

• A point where a graph intersects an axis

• A point where a graph intersects a plane

For the plane 6x + 15y + 10z = 30, what is the x-intercept?

• (0, 0, 5)

• (5, 0, 0)

• (0, 5, 0)

• (0, 0, 0)

How do you find the y-intercept of a plane equation?

• Set all variables to zero

• Set y and z to zero

• Set x and z to zero

• Set x and y to zero

What is unique about the intercepts of a sphere at the origin?

• The origin is only an x-intercept

• The origin is only a y-intercept

• The origin is not an intercept

• The origin is an intercept for all axes

How many y-intercepts does the sphere x² + (y-2)² + z² = 4 have?

• None

• One

• Two

• Three

What is a trace in 3D space?

• A line where a graph intersects a curve

• A curve where a surface intersects a plane

• A point where a surface intersects a line

• A point where a graph intersects an axis

In which plane is the xz trace found?

• None of the above

• xz plane

• xy plane

• yz plane

What shape is the trace of the plane 6x + 15y + 10z = 30 in the xy plane?

• A parabola

• A circle

• A line

• A point

What is the trace of the sphere x² + (y-2)² + z² = 4 in the xy plane?

• A circle

• A parabola

• A point

• A line

What is the trace of the sphere x² + (y-2)² + z² = 4 in the xz plane?

• A point

• A parabola

• A circle

• A line