Question

drag each label to the correct location on the grid. each label can be used more than once, but not all labels will be used. classify each of the representations of functions using the given labels. both linear neither linear linear nonlinear and nonlinear nor nonlinear x y 2 6 4 18 6 38 8 66 y = 2x + 2 x y 2 5 4 9 6 13 8 17

Explanation:

Step1: Check 1st table for linearity

Calculate rate of change:
$\frac{18-6}{4-2}=6$, $\frac{38-18}{6-4}=10$, $\frac{66-38}{8-6}=14$
Rates are not constant.

Step2: Classify 1st table

Non-constant rate = nonlinear

Step3: Check graph for linearity

Graph is a curve, not straight line = nonlinear

Step4: Check equation $y=2x+2$

Follows linear form $y=mx+b$ = linear

Step5: Check 2nd table for linearity

Calculate rate of change:
$\frac{9-5}{4-2}=2$, $\frac{13-9}{6-4}=2$, $\frac{17-13}{8-6}=2$
Rates are constant = linear

Answer:

• Top left table: nonlinear
• Top right graph: nonlinear
• Bottom left equation $y=2x+2$: linear
• Bottom right table: linear