Analyzing Proportional Relationship Graphs

Analyzing Proportional Relationship Graphs

The Price of Tomatoes

Opening

The Price of Tomatoes

These ratio tables show the relationship between the cost and weight of tomatoes at two different stores.

  • At Fruit World, the price for tomatoes is $0.60 per pound. The ratio is 0.6 : 1.
  • At Veggie Mart, the price for tomatoes is $1.15 per pound. The ratio is 1.15 : 1.
  • The formula for the cost of tomatoes at Fruit World is c = 0.6w.
  • The formula for the cost of tomatoes at Veggie Mart is c = 1.15w.

Graphs

Opening

Graphs

The graph shows both proportional relationships.

Fruit World: c = 0.6w

Veggie Mart: c = 1.15w

  • Which line represents the cost of the tomatoes at Veggie Mart?
  • Which line represents the cost of the tomatoes at Fruit World?
  • Explain how you know.

Math Mission

Opening

Analyze the graph, write the related formula, and create a table of values for a proportional relationship.

Graphs of Proportional Relationships

Work Time

Graphs of Proportional Relationships

The coordinate grid shows the graphs of five proportional relationships.

  • Approximate, as closely as possible, the constant of proportionality for each line.
  • The graph of a proportional relationship with a constant of 1 would lie between two of these lines. Explain why.

Hint:

  • If you can find one point on the line, how can you determine the constant of proportionality?
  • What would a line with a constant of proportionality of 1 look like? What are some examples of ordered pairs that have a ratio of 1?

Write a Formula

Work Time

Write a Formula

Choose one of the lines and write the formula of the line. Use x and y to name the variables.

Hint:

Once you know the constant of proportionality, how can you use it to write the formula?

Make a Table

Work Time

Make a Table

Choose a different line. Make a table that lists five pairs of values that define points on the graph.

Prepare a Presentation

Work Time

Prepare a Presentation

Prepare a presentation about what you learned about graphs and the constant of proportionality. Be sure to talk about how the constant of proportionality relates to steepness.

Challenge Problem

Make a graph with a constant of proportionality that is greater than 1.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about your classmates’ explanations for how they found the constant of proportionality, formula, table, and to explain how the constant of proportionality relates to the steepness of a line.

Hint:

As classmates present, ask questions such as:

  • How did you find the constant of proportionality based on that graph?
  • How did you figure out how to write the formula for that graph?
  • What is the ratio of any two points on a line with a constant of proportionality of 1?
  • How does the constant of proportionality relate to the steepness of the graph

The Slope

Formative Assessment

Summary of the Math: The Slope

Read and Discuss

  • In general, if quantity p is proportional to quantity q according to the formula p = kq, then the slope of the graph that represents the relationship between p and q will be equal to k, the constant of proportionality.

Hint:

Can you:

  • Explain how to find the constant of proportionality of a graph?
  • Explain how to write the formula for the graph of a proportional relationship?
  • Explain how to identify points on a graph, and create a table of values for a graph?
  • Explain the relationship between the constant of proportionality and the steepness of the graph?

The Cost of Paint

Formative Assessment

Check the Cost of Paint

The prices are proportional to the amount of paint in the cans.

Calculate the missing prices of the paint cans and the amount of paint in the last can.

Reflect On Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

An easy way to find the constant of proportionality of a graph is …