Exploring Direct Variation Equations and Graphs

This video tutorial introduces the concept of writing and graphing equations of proportional relationships. It explains how to identify direct variation, write equations from graphs, and use tables to graph equations. The lesson emphasizes the importance of the constant of proportionality and provides strategies for graphing using this constant. The tutorial concludes with encouragement to continue learning about math.

What does 'k' represent in a proportional relationship equation?

• The slope of a non-linear curve

• The variable for the y-axis

• The constant of proportionality

• The variable for the x-axis

What does it mean if an equation is in the form y = kx?

• It represents a proportional relationship

• It represents a quadratic relationship

• It represents an inverse relationship

• It represents a cubic relationship

What is a direct variation?

• A relationship where one variable is a constant multiple of the other

• A relationship where both variables increase at different rates

• A relationship where one variable decreases as the other increases

• A relationship where one variable is the square of the other

Which equation is NOT a direct variation?

• y = 1/4x

• y = 5x

• y = 3x^2

• 8y = x

Which equation represents a direct variation?

• y = x + 3

• y = x^3

• y = 3x

• y = 3/x

How do you find the constant of proportionality from a graph?

• By adding any y-coordinate to its corresponding x-coordinate

• By subtracting any y-coordinate from its corresponding x-coordinate

• By dividing any y-coordinate by its corresponding x-coordinate

• By multiplying any y-coordinate by its corresponding x-coordinate

What is the equation of a line that represents a proportional relationship passing through (2, 4)?

• y = 2x

• y = x/2

• y = 4x

• y = x + 2

How can you identify a direct variation from a table of values?

• By subtracting y values from x values

• By multiplying x and y values

• By checking if the ratio of y to x is constant

• By finding the sum of x and y values

Which of the following is a correct method to graph a direct variation?

• Using the slope-intercept form

• Drawing a curve that passes through the origin

• Only plotting points with positive x and y values

• Plotting the origin and any other point that satisfies the equation

What is the constant of proportionality in the equation y = 3x?

• 0

• 3

• x

• y