Analyzing Patterns in Functions

The video tutorial teaches how to derive linear equations from graphs using three examples: trees planted per day, cooking time for roasts, and reading pages over time. Each example demonstrates how to identify patterns in data, record them in a table, and formulate a corresponding linear equation. The tutorial emphasizes understanding the relationship between x and y values and using multiplication to find the equation.

What is the purpose of using a table when analyzing a graph?

• To avoid using equations

• To confuse the students

• To record x and y values for better analysis

• To make the graph look more colorful

In the trees planted per day example, what does the ordered pair (1, 2) represent?

• Two trees planted in one day

• Two trees planted every day

• One tree planted in two days

• One tree planted every two days

What pattern is observed in the trees planted per day example?

• The number of trees triples each day

• The number of trees remains constant

• The number of trees decreases each day

• The number of trees doubles each day

What is the correct equation for the trees planted per day example?

• y = x / 2

• y = x + 1

• y = x - 1

• y = 2x

In the cooking time example, what does the ordered pair (2, 1) represent?

• Two hours to cook one pound

• One hour to cook two pounds

• One pound cooked in two hours

• Two pounds cooked in two hours

What pattern is observed in the cooking time example?

• Cooking time doubles with each pound

• Cooking time is proportional to weight

• Cooking time halves with each pound

• Cooking time remains constant

What is the correct equation for the cooking time example?

• y = x - 2

• y = 2x

• y = x / 2

• y = x + 2

In the reading time example, what does the ordered pair (1, 60) represent?

• 60 pages read every minute

• One page read every 60 seconds

• 60 pages read in one hour

• One page read in 60 minutes

What pattern is observed in the reading time example?

• Pages read decreases every hour

• Pages read doubles every hour

• Pages read is proportional to time

• Pages read remains constant

What is the correct equation for the reading time example?

• y = x + 60

• y = x / 60

• y = 60x

• y = x - 60