Direction Fields and Slope Analysis

The video tutorial explains how to determine the slope of a direction field for a given differential equation at specific points. It calculates the slope at points (1, 1.5) and (0.5, 1.5), and uses these values to identify the correct direction field. The tutorial concludes by verifying the slopes at additional points to ensure the correct field is chosen.

What is the slope of the direction field at the point (1, 1.5) for the differential equation dydx = y - x?

• -2.5

• 2.5

• 0

• 1

Which of the following is NOT a possible slope for the direction field at the point (1, 1.5)?

• 0

• 1

• 2.5

• -2.5

At the point (0.5, 1.5), what is the slope of the direction field?

• -2

• 0

• 2

• 1

What is the derivative function value at the point (0.5, 1.5)?

• 2

• 1

• -1

• 0

Which of the following points is used to verify the correct direction field by comparing slopes?

• (1, 1)

• (0, 0)

• (2, 2)

• (-1, -1)

What is the slope of the direction field at the point (1, 1) for the differential equation dydx = y - x?

• 2

• -1

• 0

• 1

Which point is used to eliminate incorrect direction fields based on slope analysis?

• (-1, -1)

• (1, 1)

• (1, 1.5)

• (0.5, 1.5)

What is the significance of the slope at the point (1, 1) in determining the correct direction field?

• It eliminates a field

• It confirms the field

• It is a midpoint

• It is irrelevant

How is the slope at the point (-1, -1) verified in the context of the direction field?

• It is positive

• It is negative

• It is zero

• It is undefined

What is the slope of the direction field at the point (-1, -1)?

• 2

• -1

• 0

• 1