Exploring Direct Variation and Proportionality

The video tutorial covers the concept of direct variation, explaining it as a proportional relationship represented by the equation y = kx. The constant k, also known as the constant of proportionality, is calculated by dividing y by x. The tutorial demonstrates how to verify if a set of data points forms a direct variation by checking if the constant k remains consistent across all pairs. The video concludes with forming the equation of direct variation and emphasizes the importance of understanding proportional relationships.

What is the formula for direct variation?

• y = k / x

• y = k * x

• y = k - x

• y = k + x

What does the constant of proportionality (k) represent in direct variation?

• The unit rate

• The y-intercept

• The x-intercept

• The slope of the line

How do you calculate the constant of proportionality (k) from a table of values?

• Divide y by x

• Subtract y from x

• Add y and x

• Multiply y by x

If y = 0.87 and x = 12, what is the value of k?

• 0.725

• 0.0725

• 0.00725

• 7.25

Why is it important to check each pair of values in a table when verifying a proportional relationship?

• To ensure all values are positive

• To confirm the relationship is linear

• To verify the relationship is proportional

• To check for any outliers

What is the result of 0.29 divided by 4?

• 0.29

• 0.00725

• 0.725

• 0.0725

What is the opposite operation of dividing when checking the proportional relationship?

• Squaring

• Multiplying

• Subtracting

• Adding

What is the value of 0.0725 times 36?

• 0.0261

• 26.1

• 0.261

• 2.61

What is the equation of direct variation if k = 0.0725?

• y = 0.0725 / x

• y = 0.0725 - x

• y = 0.0725 + x

• y = 0.0725 * x

How is the constant of proportionality (k) found?

• By dividing y by x

• By multiplying y by x

• By subtracting y from x

• By adding y and x