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

Answer:

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

Step-by-step 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.

Answer 2

Answer:

Sample Answer:When a linear function is expressed in different forms, its slope and y-intercept remain the same. The slope from the equation is -1, and the y-intercept from the equation is 3. The slope from the table is -1, and the y-intercept from the table is −3. These are not the same functions.

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Step-by-step explanation: