Understanding Linear Functions and Slopes

The video tutorial explains how to determine if a function represented in a table is linear. It covers calculating the slope by dividing the change in function values by the change in x-values, ensuring this ratio remains constant for linear functions. If the function is not linear, 'DN' is entered for the slope. The tutorial includes examples of both linear and non-linear functions, with graphical verification for linearity. The key takeaway is understanding how to identify linear functions and calculate their slopes.

What must remain constant for a function to be considered linear?

• The change in X

• The change in Y

• The ratio of change in Y to change in X

• The sum of X and Y

If the change in function value is 8.5 and the change in X is 1, what is the slope?

• 7.5

• 10.5

• 8.5

• 9.5

What is the slope when the change in function value is 59.5 and the change in X is 7?

• 7.5

• 10.5

• 8.5

• 9.5

How can you verify the linearity of a function graphically?

• By plotting points and checking if they form a triangle

• By plotting points and checking if they form a line

• By plotting points and checking if they form a circle

• By plotting points and checking if they form a square

In the second example, what is the change in function value when X changes from 3 to 9?

• 24

• 6

• 43

• 19

What is the slope when the change in function value is 24 and the change in X is 6?

• 3

• 4

• 5

• 6

What indicates that a function is not linear in the second example?

• The ratio of change in function value to change in X is not constant

• The change in function value is constant

• The sum of X and function value is constant

• The change in X is constant

What should be entered for the slope if a function is not linear?

• NL

• ND

• DN

• LN

What is the change in X when it goes from 9 to 11 in the second example?

• 4

• 2

• 1

• 3

What is the change in function value when it goes from 43 to 47 in the second example?

• 5

• 3

• 2

• 4