Determining Direct Variation: Equations, Tables, and Graphs

What is the form of a direct variation equation?

• y = kx

• y = x^2

• y = mx + b

• y = k/x

Which of the following is a direct variation equation?

• y = 2x + 3

• y = -3x

• y = 4/x

• y = x^2 + 1

If an equation has a constant term (e.g., y = 2x - 4), is it a direct variation?

• Yes

• No

• Sometimes

• Depends on the value of the constant

In a direct variation equation, can the constant of variation (k) be a fraction?

• Only if it is a proper fraction

• No

• Yes

• Only if it is an improper fraction

What is the key feature of a direct variation when looking at a table of values?

• The x-values and y-values are both increasing

• The y-values are all positive

• The x-values are all positive

• The table includes the point (0,0)

If a table of values does not explicitly show (0,0), what should you do?

• Check if the x-values are all positive

• Interpolate or extrapolate to check if (0,0) would be included

• Ignore the table

• Assume it is not a direct variation

Which of the following tables represents a direct variation?

• x: 1, 2, 3; y: 2, 4, 6

• x: 1, 2, 3; y: 3, 5, 7

• x: 0, 1, 2; y: 1, 2, 3

• x: -1, 0, 1; y: 1, 0, -1

What is the main indicator that a graph represents a direct variation?

• The line has a positive slope

• The line passes through the origin

• The line is vertical

• The line is horizontal

If a graph of a direct variation has a slope of 3/2, what is the equation of the line?

• y = -3/2x

• y = 3/2x

• y = 2x/3

• y = 2/3x

For a direct variation graph with a slope of -4, what is the equation?

• y = 4x

• y = -x/4

• y = -4x

• y = x/4