Exploring Equations for Proportional Relationships

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 ratios are consistent and from graphs by ensuring the line passes through the origin. The video also clarifies that equations with additional terms are not proportional.

What is the first step in recognizing a proportional relationship from a table?

• Check if the table values reduce to the same ratio.

• Check if the table values are all different.

• Check if the table values are all positive.

• Check if the table values are all integers.

What is the form of an equation that represents a proportional relationship?

• y = m + x

• y = x + b

• y = mx

• y = mx + b

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

• y

• 0

• x

• 5

Which of the following equations does NOT represent a proportional relationship?

• y = 0.5x

• y = 4x + 1

• y = -3x

• y = 2x

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

• By dividing each pair of values and checking if they reduce to the same ratio.

• By multiplying all the values in the table.

• By adding all the values in the table.

• By subtracting the smallest value from the largest value.

If a table of values reduces to the same ratio, what does this ratio represent?

• The constant of proportionality.

• The slope of the line.

• The x-intercept.

• The y-intercept.

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

• It must be a straight line that passes through the origin.

• It must be a curved line.

• It must pass through the y-axis.

• It must pass through the x-axis.

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

• By finding the point where the line crosses the y-axis.

• By finding the x-intercept.

• By finding the slope of the line.

• By finding the y-intercept.

If a graph passes through the origin and is a straight line, what can be concluded?

• It represents a non-proportional relationship.

• It represents a proportional relationship.

• It represents a quadratic relationship.

• It represents an exponential relationship.

What is the equation for a proportional relationship if the constant of proportionality is 4?

• y = 4x

• y = x + 4

• y = 4x + 1

• y = 4 + x