Question

1. which of these represents a linear function?

a. (1,6), (5,3), (8,1), (1,2)
b. $y = 6x - 1$
c. image of a parabola
d.

x	3	3	3	3
y	1	2	3	4

Explanation:

Step1: Analyze Option a

A function must have each input (x - value) with exactly one output (y - value). In option a, the x - value 1 has two y - values (6 and 2), so it is not a function, let alone a linear function.

Step2: Analyze Option b

The equation \(y = 6x-1\) is in the form of a linear function \(y=mx + b\), where \(m = 6\) (slope) and \(b=- 1\) (y - intercept). Linear functions have a constant rate of change (slope) and their graphs are straight lines.

Step3: Analyze Option c

The graph in option c is a parabola, which is the graph of a quadratic function (\(y = ax^{2}+bx + c\) with \(a
eq0\)), not a linear function.

Step4: Analyze Option d

In option d, the x - value 3 is repeated for different y - values. Also, the rate of change is not constant (for a linear function, \(\frac{\Delta y}{\Delta x}\) should be constant). Here, \(\Delta x = 0\) (since x is always 3) and \(\Delta y\) changes, so it is not a linear function.

Answer:

b. \(y = 6x-1\)