Question

1. $y = 2x + 1$

this is (circle one) linear or nonlinear.

x(input)	-2	-1	0	1	2
y(output)
$(x,y)$

1. $y = x$

this is (circle one) linear or nonlinear.

x(input)	-2	-1	0	1	2
$(x,y)$

Explanation:

Step1: Fill table for \(y=2x+1\)

Substitute \(x=-2,-1,0,1,2\):

• \(x=-2\): \(y=2(-2)+1=-3\)
• \(x=-1\): \(y=2(-1)+1=-1\)
• \(x=0\): \(y=2(0)+1=1\)
• \(x=1\): \(y=2(1)+1=3\)
• \(x=2\): \(y=2(2)+1=5\)

Step2: Fill table for \(y=x\)

Substitute \(x=-2,-1,0,1,2\):

• \(x=-2\): \(y=-2\)
• \(x=-1\): \(y=-1\)
• \(x=0\): \(y=0\)
• \(x=1\): \(y=1\)
• \(x=2\): \(y=2\)

Step3: Check linearity

Both \(y=2x+1\) and \(y=x\) are linear (degree 1 polynomials).

Answer:

Table for \(y=2x+1\)

x(input)	-2	-1	0	1	2
(x,y)	(-2,-3)	(-1,-1)	(0,1)	(1,3)	(2,5)

Linearity: linear

Table for \(y=x\)

x(input)	-2	-1	0	1	2
(x,y)	(-2,-2)	(-1,-1)	(0,0)	(1,1)	(2,2)

Linearity: linear