Proportional Relationships and Constants

The video tutorial covers proportional relationships in eighth grade math, explaining the concept through graphs, tables, and equations. It introduces the constant of proportionality, K, and demonstrates how to use it in equations. The tutorial provides practical examples and emphasizes that proportional relationships always pass through the origin on a graph. The lesson concludes with a summary of key points and an invitation to watch the next video on the rate of change.

What is a proportional relationship?

• A relationship where the ratio between two variables is constant.

• A relationship where the sum of two variables is constant.

• A relationship where one variable is always greater than the other.

• A relationship where the difference between two variables is constant.

In the equation y = kx, what does 'k' represent?

• The product of x and y

• The sum of x and y

• The constant of proportionality

• The difference between x and y

If k = 0.5 in a proportional relationship, what is y when x = 10?

• 20

• 15

• 10

• 5

How do you find the constant of proportionality from a table?

• Divide y by x for each pair of values

• Multiply x and y for each pair of values

• Add x and y for each pair of values

• Subtract x from y for each pair of values

What is the output when x = 20 in the equation y = 0.5x?

• 20

• 5

• 10

• 15

What is the significance of the origin in a graph of a proportional relationship?

• It is where the line ends.

• The line always passes through it.

• It is where the line starts.

• It is the midpoint of the line.

In a proportional relationship with k = 2, what is y when x = 3?

• 3

• 4

• 6

• 5

How do you determine the value of k from a graph?

• By finding the y-intercept

• By finding the x-intercept

• By finding the midpoint of the line

• By finding the slope of the line

If y = 2x, what is y when x = 5?

• 20

• 15

• 10

• 5

What does a constant rate of change mean in a proportional relationship?

• The rate of change is negative

• The rate of change is constant for all x

• The rate of change is zero

• The rate of change varies with x