Question

Compare the linear functions expressed by the equation, y = –x + 3, and by data in the table.

A 2-column table with 4 rows. Column 1 is labeled x with entries negative 4, negative 2, 1, 3. Column 2 is labeled y with entries 1, negative 1, negative 4, negative 6.

Explain how to determine if these two are the same function expressed in different ways

Answer 1

The slope formula is y2 - y1/x2 - x1.

Explanation:

First plug in x = 1, x = 2, and x = 3 in to the equation y = 4x to find the first 3 points(Like the first three are shown for the table.) which are (1, 4), (2, 8), and (3, 12).

The slope of the table would be 9 - 3/3 - 1, after subtracting you get 6/2. You would then divide 6 by 2, which gives you 3. 3 is the slope of the table.

The slope of the equation goes through the same process. 12 - 4/3 - 1, after subtracting it's 8/2, and after dividing you get 4. The slope of the equation is 4.

This means the equation has the greater slope.