Question

Create two equations, one that will model a linear relation and one that will not (e.g., y = -3x +2, y = 4x2 -7). Describe the ways by which you could determine whether it is a linear relation. Include calculations, graphs, tables of values and anything else you feel will support your argument.

Answer 1

linear: y = x + 1

non-linear: y = x² + 1

Explanation:

In a linear relationship, from one pair (x1,y1) to other one (x2,y2) that satisfies the equation, there is a constant k, so that k = (y2 - y1)/(x2 - x1).

Equation: y = x + 1

Computing some points as an example:

x | y

0 | 1

1 | 2

2 | 3

3 | 4

(2-1)/(1-0) = (3-2)/(2-1) = (4-3)/(3-2) = 1. Therefore, the equation is linear.

Equation: y = x² + 1

Computing some points as an example:

x | y

0 | 1

1 | 2

2 | 5

3 | 10

(2-1)/(1-0) ≠ (5-2)/(2-1) ≠ (10-5)/(3-2). Therefore, the equation is not linear.