Understanding Linear Functions

The video tutorial explains how to determine if tables represent linear functions. It covers the criteria for a function and linearity, using tables A to E as examples. For each table, the video checks if each input has a single output and if the slope is consistent. It provides equations for tables that are linear functions and explains why others are not.

What are the two main criteria for a table to represent a linear function?

• It must be linear and have a consistent y-value.

• It must be linear and a function.

• It must be linear and have a positive slope.

• It must be a function and have a y-intercept of zero.

In Table A, what is the slope of the linear function?

• 3/4

• 2/3

• 1/3

• 1/2

What is the y-intercept of the linear function derived from Table A?

• 8

• 5

• 6

• 7

Why is Table B not considered a function?

• It has inconsistent y-values.

• It has a negative slope.

• It has multiple y-values for the same x-value.

• It has a zero slope.

What is the slope of the linear function derived from Table C?

• -2/5

• 2/5

• -1/3

• 1/3

What is the y-intercept of the linear function derived from Table C?

• -4

• -6

• -8

• -10

Why is Table D not considered linear?

• It has a zero slope.

• It has a negative slope.

• Its slope is not consistent.

• It has multiple y-values for the same x-value.

What is the slope of the linear function derived from Table E?

• 3/4

• 1/2

• 2/3

• 1/3

What is the y-intercept of the linear function derived from Table E?

• 7

• 8

• 6

• 5

What are the steps to determine if a table represents a linear function?

• Check if it is linear, find the slope, check if it is a function.

• Check if it is a function, check if it is linear, find the slope and y-intercept.

• Find the slope, check if it is a function, find the y-intercept.

• Check if it is a function, find the y-intercept, check if it is linear.