Direct and Partial Variation Concepts

The video tutorial explains how to identify direct and partial variations using equations, graphs, and tables. It covers three equations: y = 1/2x, y = 2 - x, and 2x - y = 0. The tutorial demonstrates that y = 1/2x and 2x - y = 0 are direct variations as they pass through the origin, while y = 2 - x is a partial variation due to its y-intercept not being zero. The video emphasizes the importance of understanding the form of equations and graphing to distinguish between these variations.

What is the main focus of the video tutorial?

• Understanding quadratic equations

• Exploring polynomial functions

• Identifying direct and partial variations

• Learning about trigonometric functions

Which equation represents a direct variation?

• y = x^2 + 3

• y = 1/2x

• y = 3x + 2

• y = 2 - x

What is the characteristic of a direct variation equation?

• It has a negative slope

• It forms a parabola

• It passes through the origin

• It has a constant y-intercept

How can you graphically justify that y = 1/2x is a direct variation?

• The graph is a vertical line

• The graph is a parabola

• The graph is a straight line through the origin

• The graph is a horizontal line

What is the y-intercept of the equation y = 2 - x?

• 2

• 0

• 1

• -1

Why is y = 2 - x considered a partial variation?

• It has a constant slope

• It forms a quadratic curve

• It does not pass through the origin

• It has a y-intercept of 0

What is the slope of the line represented by y = 2 - x?

• -1

• 0

• 2

• 1

How can you rearrange the equation 2x - y = 0 to identify its variation type?

• y = 2 - x

• y = x/2

• y = x + 2

• y = 2x

What does the equation 2x - y = 0 represent?

• A constant function

• A direct variation

• A partial variation

• A quadratic variation

What is a key feature of a direct variation graph?

• It is a horizontal line

• It is a curve

• It passes through the origin

• It has a y-intercept of 2