How do you write ordered pairs as a function: (-19,-12), (-12,-5), (-5,2), (2,9), and (9,16)?

1 Answer
George C.
May 6, 2016

#f(x) = x+7#

Explanation:

Notice that both the #x# coordinates and #y# coordinates are in arithmetic sequence:

  • #bb(x: ) -19, -12, -5, 2, 9# with common difference #7#

  • #bb(y: ) -12, -5, 2, 9, 16# with common difference #7#

Since #y# is increasing at the same rate as #x#, the slope is #1# and we can see that the offset between the values in the two sequences is also #7#.

Hence, in slope intercept form we have:

#y = x+7#

or in function notation:

#f(x) = x+7#

graph{(y-x-7)((x+19)^2+(y+12)^2-0.2)((x+12)^2+(y+5)^2-0.2)((x+5)^2+(y-2)^2-0.2)((x-2)^2+(y-9)^2-0.2)((x-9)^2+(y-16)^2-0.2) = 0 [-39.67, 40.33, -17.12, 22.88]}

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