On a recent test, you were given the table displayed and asked to write the rule that models it.
What should the rule be for the table?
O Subtract 6 from the x value to get the y value.
O Multiply the x value by 1/2 to get the y value.
O Multiply the x value by 1/4 to get the y value.
O Add 6 to the value to get the y value.

9514 1404 393

  A.  Subtract 6 from the x value to get the y value.

Step-by-step explanation:

Sometimes, it works well to simply try the answers to see what works. Sometimes, it works better to use a point other than the first or second.

Using the last point (x, y) = (16, 10), we can try the rules:

  subtract 6 from x: 16 -6 = 10 . . . this rule works

  multiply by 1/2: 16×1/2 = 8, not 10 . . . doesn't work

  multiply by 1/4: 16×1/4 = 4, not 10 . . . doesn't work

  add 6 to x: 16 +6 = 22, not 10 . . . doesn't work

The only rule that works is ...

  Subtract 6 from the x value to get the y value.

Additional comments

You cannot always assume the table represents a linear function. In this case, all of the answer choices are linear functions, so that is a reasonable assumption. The x-values all have the same difference: 4. The y-values also all have the same difference: 4. So the slope of the line is 4/4 = 1, which tells you right away that "multiply by 1/2" and "multiply by 1/4" will be wrong.

The x-values are all greater than the y-values, so "add 6 to the x value" will not be correct. Since the slope is 1, the difference between x and y will be a constant, easily found from any table entry.

  y = x + b . . . . equation of a line with a slope of 1

  2 = 8 + b . . . . using the first table entry

  -6 = b . . . . . . . subtract 8

Then ...

  y = x - 6