Exploring Linear and Nonlinear Functions

The video tutorial explores whether a given table represents a linear equation by examining changes in x and y values. It explains the concept of delta as a shorthand for change and emphasizes the need for a constant ratio between changes in y and x for linearity. The tutorial checks this ratio across different data points, ultimately concluding that the equation is not linear due to a varying rate of change in the last set of points.

What is the main question being addressed in the video?

• Does the table represent a logarithmic equation?

• Does the table represent a quadratic equation?

• Does the table represent an exponential equation?

• Does the table represent a linear equation?

What is the value of y when x is -7?

• 3

• 4

• 7

• 1

What is the change in x when moving from -7 to -3?

• Increase by 3

• Decrease by 4

• Increase by 4

• Decrease by 3

What is the change in y when x increases by 4 from -7 to -3?

• Decrease by 1

• Increase by 1

• Increase by 4

• Decrease by 4

What must be constant for the table to represent a linear equation?

• The ratio of change in y to change in x

• The sum of x and y

• The product of x and y

• The difference between x and y

What is the ratio of change in y to change in x for the first set of points?

• -1/4

• 1/4

• -4

• 4

What is the change in x when moving from -3 to 1?

• Decrease by 4

• Increase by 4

• Increase by 3

• Decrease by 3

What is the change in y when x increases by 4 from -3 to 1?

• Increase by 4

• Decrease by 1

• Decrease by 4

• Increase by 1

What is the change in x when moving from 1 to 7?

• Decrease by 4

• Increase by 6

• Decrease by 6

• Increase by 4

Why does the table not represent a linear equation?

• Because the sum of x and y is constant

• Because the ratio of change in y to change in x is not constant

• Because the ratio of change in y to change in x is constant

• Because the product of x and y is constant