Exploring Linear Functions

The video tutorial explains linear functions, their characteristics, and how to identify them. It covers the standard form of linear equations and highlights that linear functions create a line when graphed. The tutorial provides examples to distinguish between linear and non-linear functions by examining constant changes in x and y values. The lesson concludes with a summary and a practice problem to reinforce understanding.

What is the basic definition of a linear function?

• A function that creates a curve when graphed

• A function that has variables in the denominator

• A function that creates a line when graphed

• A function that includes exponents greater than one

Which of the following represents the standard form of a linear equation?

• ax^2 + by + c = 0

• ax + by = c

• ax + by^2 = c

• ax^2 + by^2 = c

In the standard form of a linear equation, which of the following is true?

• X and Y have exponents greater than one

• X and Y are multiplied together

• X and Y do not appear in the denominator of a fraction

• X and Y are under a radical or square root symbol

What does a constant change in X corresponding to a constant change in Y represent?

• The slope of a linear function

• The intercept of a linear function

• The asymptote of a function

• The curvature of a function

How can you determine if a set of ordered pairs represents a linear function?

• By checking if X and Y are under a radical

• By finding a constant change in X and Y

• By checking if the points form a curve

• By ensuring X and Y are in the denominator

In the example where X goes from -2 to 2 and Y goes from 7 to -2, what is the constant change in Y?

• Adding 1

• Subtracting 1

• Subtracting 3

• Adding 3

In the example where X increases by 1 but Y does not have a constant change, what can be concluded?

• The points satisfy a linear function

• The points do not satisfy a linear function

• The points form a curve

• The points are undefined

When organizing ordered pairs in a table, what pattern indicates a linear function?

• A variable change in both X and Y

• A constant change in X and a variable change in Y

• A variable change in X and a constant change in Y

• A constant change in both X and Y

In the final example, what is the constant change in X?

• Adding 4

• Adding 5

• Adding 3

• Adding 2

What is the key takeaway from the lesson on linear functions?

• X and Y must be in the denominator

• Linear equations create a curve when graphed

• Linear functions always have exponents greater than one

• A constant change in X corresponds to a constant change in Y