Writing and Graphing Equations of Proportional Relationships

This video tutorial covers proportional relationships and direct variation, explaining how to write and identify equations of direct variation from tables, graphs, and equations. It introduces the concept of constant proportionality and demonstrates graphing techniques using tables and constants. The tutorial emphasizes the importance of the equation form y = kx and provides strategies for identifying and graphing direct variation.

What is one of the main objectives of the lesson on proportional relationships?

• To write the equation of a proportional relationship from a table or a graph

• To learn about geometric shapes

• To solve quadratic equations

• To understand the history of mathematics

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

• The slope of the line

• The constant of proportionality

• The x-coordinate

• The y-intercept

What is the form of a direct variation equation?

• y = mx + b

• y = kx

• y = ax^2 + bx + c

• y = x^2

Which of the following is NOT a direct variation?

• y = 7x

• y = 0.5x

• y = 3x^2

• y = 5x

How can you identify the constant of proportionality from a graph?

• By counting the number of points on the line

• By finding the y-intercept

• By calculating the slope of the line

• By identifying the x-intercept

What is the first step in writing an equation from a graph?

• Calculate the area under the curve

• Find the midpoint of the line

• Identify the constant of proportionality

• Identify the y-intercept

When graphing a direct variation, what is always a point on the line?

• (0, 0)

• (1, 1)

• (1, 0)

• (0, 1)

What is the relationship between the constant of proportionality and ordered pairs on a graph?

• The constant is the difference between y and x

• The constant is the product of the ordered pairs

• The constant is the ratio of y to x in the ordered pairs

• The constant is the sum of the ordered pairs

Which strategy can be used to graph a line when given an equation?

• Using the quadratic formula

• Calculating the area under the curve

• Identifying the constant of proportionality and plotting points

• Finding the midpoint of the line

If a line passes through the origin and has a constant of proportionality of 2/5, what is the equation of the line?

• y = 2x

• y = 2/5x

• y = 5/2x

• y = 5x