Exploring Patterns and Writing Explicit Expressions

The video tutorial explains how to define explicit expressions by exploring patterns. It covers the slope-intercept form of linear equations, identifying the slope and y-intercept from a table of values, and writing explicit expressions using the rate of change and initial value. The tutorial also addresses common misunderstandings and provides examples to practice using explicit expressions to calculate areas of figures.

What does the letter 'm' represent in the slope-intercept form of a linear equation?

• The slope

• The y-intercept

• The independent variable

• The dependent variable

How is the rate of change determined from a table of values?

• By adding the x and y values

• By dividing the change in y by the change in x

• By subtracting the x values from the y values

• By multiplying the x and y values

What is the explicit expression for a pattern where the area increases by 3 each time?

• f(x) = 3x + 1

• f(x) = 4x + 1

• f(x) = 3x

• f(x) = x + 3

How can you find the area of 50 L-shaped figures using an explicit expression?

• By adding the areas of each figure

• By using the expression f(x) = 3x and substituting x with 50

• By using the expression f(x) = 4x + 1

• By creating a table of values up to 50

Which of the following is a common misunderstanding about explicit expressions?

• They describe a pattern to find any term

• They always have the form f(x) = mx + b

• They require knowing the previous term

• They can only be used for linear patterns

What is the initial value in the pattern where the area of the first figure is 5 and the rate of change is 4?

• 4

• 1

• 5

• 0

How do you express repeated addition in an explicit expression?

• By writing each addition separately

• By using multiplication

• By using division

• By using subtraction