Direct Variation

What is the definition of direct variation?

• Direct variation is a mathematical relationship between two variables where one variable is a constant difference of the other.

• Direct variation is a mathematical relationship between two variables where one variable is a constant sum of the other.

• Direct variation is a mathematical relationship between two variables where one variable is a constant quotient of the other.

• Direct variation is a mathematical relationship between two variables where one variable is a constant multiple of the other.

How can you graph direct variation equations?

• Graph the points and connect them with a curved line.

• Use a scatter plot to connect the points.

• Plot the points and connect them with a zigzag line.

• Plot the points and connect them with a straight line.

Given a table, how can you identify direct variation?

• Check if the sum of y-values and x-values is constant.

• Check if the difference between y-values and x-values is constant.

• Check if the product of y-values and x-values is constant.

• Check if the ratio of y-values to x-values is constant.

Write the direct variation equation for the following scenario: y varies directly with x, and y = 6 when x = 2.

• y = 3x

• y = 8x

• y = 4x

• y = 2x

What are some applications of direct variation in real life?

• Speed and time, Cost and quantity, Fuel consumption and distance

• Age and income

• Height and weight

• Temperature and humidity

True or False: In a direct variation equation, the constant of variation is always positive.

• Sometimes

• Negative

• True

• False

If y varies directly with x, and y = 10 when x = 5, what is the value of y when x = 8?

• 16

• 30

• 25

• 20

What is the graph of a direct variation equation?

• A parabola

• A circle

• A hyperbola

• A straight line passing through the origin (0,0)

If y varies directly with x, and y = 12 when x = 3, what is the value of x when y = 18?

• 2

• 6

• 9

• 4

Explain how to write a direct variation equation given a scenario.

• Identify two variables that are inversely proportional and write the equation in the form y = k/x.

• Identify two variables that are not related and write the equation in the form y = mx + b.

• Identify two variables that are indirectly proportional and write the equation in the form y = k/x^2.

• Identify two variables that are directly proportional and write the equation in the form y = kx.