Back to Interpret the equation y = mx + b as defining a linear function — Problem 2 · Task Set 47

8.F.A.3 Tutor Intake -- Linear vs. Nonlinear Functions

This short check helps your tutor see where to start. Work each problem on
your own, without a calculator. If you are not sure, give your best try —
every answer helps your tutor plan your first few sessions.

Grade 8·7 problems·~8 min·Common Core Math - Grade 8·container·8-f-a-3

Work through problems with immediate feedback

Procedures

A function is shown in this table:

x: 1, 2, 4, 7
y: 3, 5, 9, 15

The y-differences are 2, 4, 6 -- they look non-constant. Is this
function linear or nonlinear?

Nonlinear -- the y-differences (2, 4, 6) are not constant.

Nonlinear -- the x-values do not increase by the same amount each row, so the function cannot be linear.

Linear -- the x-steps are 1, 2, 3, and computing (change in y)/(change in x) for each gives 2/1 = 2, 4/2 = 2, 6/3 = 2, which is constant.

It cannot be determined without a graph.