Creating Equations from Proportional Relationships

The video tutorial explains how to solve questions on proportional relationships using tables. It covers the concept of proportional equations, the constant of proportionality (k), and provides multiple examples to illustrate how to verify and solve these relationships. The tutorial also discusses how to handle non-proportional relationships and use decimals in calculations. The video concludes with a final example to reinforce the learning objectives.

What is the general form of the equation for a proportional relationship?

• y = k * x

• y = x / k

• y = k + x

• y = k / x

If y = 5x, what is the constant of proportionality?

• 0.5

• 5

• 1

• 10

Given the table: (x, y) = (2, 8), (3, 12), (4, 16), (5, 20), what is the equation of the proportional relationship?

• y = 5x

• y = 3x

• y = 4x

• y = 2x

For the table (x, y) = (6, 12), (7, 14), (8, 16), (9, 18), what is the constant of proportionality?

• 3

• 4

• 2

• 1

If k = 0.6, which of the following tables represents this proportional relationship?

• (x, y) = (1, 0.6), (2, 1.2), (3, 1.8), (4, 2.4)

• (x, y) = (1, 0.5), (2, 1.0), (3, 1.5), (4, 2.0)

• (x, y) = (1, 0.7), (2, 1.4), (3, 2.1), (4, 2.8)

• (x, y) = (1, 0.8), (2, 1.6), (3, 2.4), (4, 3.2)

What is the equation of the proportional relationship if k = 0.16?

• y = 1.6x

• y = 0.6x

• y = 0.16x

• y = 16x

If the ratios of y to x are not constant, what can we conclude?

• The relationship is proportional

• The relationship is not proportional

• The constant of proportionality is zero

• The constant of proportionality is one

Given the table (x, y) = (1, 19), (2, 29), (3, 39), (4, 49), is the relationship proportional?

• Yes, because the values increase

• No, because the ratios are not constant

• Yes, because the ratios are constant

• No, because the values decrease

If the constant of proportionality is 25, what is the equation of the relationship?

• y = 0.25x

• y = 2.5x

• y = 250x

• y = 25x

Which of the following tables represents a proportional relationship with k = 14?

• (x, y) = (1, 13), (2, 26), (3, 39), (4, 52)

• (x, y) = (1, 12), (2, 24), (3, 36), (4, 48)

• (x, y) = (1, 15), (2, 30), (3, 45), (4, 60)

• (x, y) = (1, 14), (2, 28), (3, 42), (4, 56)