Fill in the blank(s) to correctly complete each sentence, or answer the question as appropriate. In the equation y = 6x, y varies directly as x. When x=5, y=30. What is the value of y when x=10?

Key Concepts

Direct Variation

Direct variation describes a relationship between two variables where one variable is a constant multiple of the other. In the equation y = kx, k is the constant of variation. This means that as x increases, y increases proportionally, and vice versa. Understanding this concept is crucial for solving problems involving proportional relationships.

Substituting Values

Substituting values involves replacing a variable in an equation with a specific number to find the value of another variable. In the context of the equation y = 6x, substituting x with a known value allows us to calculate the corresponding value of y. This technique is essential for solving equations and understanding how changes in one variable affect another.

Proportional Relationships

Proportional relationships occur when two quantities maintain a constant ratio. In the equation y = 6x, the ratio of y to x is always 6, indicating that for every unit increase in x, y increases by 6 units. Recognizing these relationships helps in predicting values and understanding the behavior of linear equations.