without graphing, determine if the following data set is exactly linear, approximately linear, or…

without graphing, determine if the following data set is exactly linear, approximately linear, or nonlinear.\n|x|y|\n|1|5|\n|2|7|\n|3|14|\n|4|7|\n|5|5|\nis the data set exactly linear, approximately linear, or nonlinear?\napproximately linear\nexactly linear\nnonlinear

without graphing, determine if the following data set is exactly linear, approximately linear, or nonlinear.\n|x|y|\n|1|5|\n|2|7|\n|3|14|\n|4|7|\n|5|5|\nis the data set exactly linear, approximately linear, or nonlinear?\napproximately linear\nexactly linear\nnonlinear

Answer

Explanation:

Step1: Calculate first - differences of y - values

For (x = 1) to (x = 2), (\Delta y_1=7 - 5=2); for (x = 2) to (x = 3), (\Delta y_2=14 - 7 = 7); for (x = 3) to (x = 4), (\Delta y_3=7 - 14=-7); for (x = 4) to (x = 5), (\Delta y_4=5 - 7=-2).

Step2: Analyze the first - differences

In a linear function, the first - differences of (y) values for equally - spaced (x) values are constant. Here, the first - differences (2,7, - 7,-2) are not constant.

Answer:

Nonlinear