Proportional Relationships and Constants

The video tutorial explains how to recognize proportional relationships in equations, tables, and graphs. It emphasizes that a proportional relationship can be represented by an equation of the form y = kx, where k is the constant of proportionality. The tutorial demonstrates how to identify this constant from tables by checking if the ratios are consistent and from graphs by ensuring the line passes through the origin. The video provides examples to illustrate these concepts.

What is a key characteristic of a proportional relationship when represented in an equation?

• It includes a constant term.

• It has a variable exponent.

• It is a linear equation passing through the origin.

• It is a quadratic equation.

Which of the following equations represents a proportional relationship?

• y = 2x - 1

• y = 3x + 2

• y = x^2

• y = 5x

How can you determine the constant of proportionality from a table of values?

• By subtracting each x-value from its corresponding y-value.

• By multiplying each x-value by its corresponding y-value.

• By dividing each y-value by its corresponding x-value and checking for consistency.

• By finding the sum of all values.

What is the constant of proportionality if the table shows pairs (16, 4), (20, 5), (24, 6), and (28, 7)?

• 3

• 5

• 2

• 4

What must be true for a graph to represent a proportional relationship?

• It must be a parabola.

• It must have a positive slope.

• It must pass through the origin and be a straight line.

• It must be a horizontal line.

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

• By finding the y-intercept.

• By finding the slope of the line.

• By checking the x-intercept.

• By measuring the angle of the line.

If a graph passes through the origin and has a point (1, 4), what is the constant of proportionality?

• 4

• 3

• 2

• 1

What is the equation of a line with a constant of proportionality of 4?

• y = x/4

• y = 4x + 1

• y = x + 4

• y = 4x

Which method is NOT used to verify a proportional relationship?

• Ensuring all ratios in a table are equal.

• Calculating the constant of proportionality.

• Checking if the graph is a straight line through the origin.

• Finding the y-intercept of the graph.

What should you do if the equation has an extra term, like y = 2x + 7?

• Consider it a proportional relationship.

• Recognize it as not a proportional relationship.

• Multiply the extra term by x.

• Ignore the extra term.