Question

is the function $y = -\frac{9}{8} + \frac{1}{6x}$ linear or nonlinear? linear nonlinear

Explanation:

Step1: Recall linear function form

A linear function has the form \( y = mx + b \), where \( m \) and \( b \) are constants, and \( x \) is to the first power (degree 1), with no variable in the denominator.

Step2: Analyze given function

The given function is \( y = -\frac{9}{8} + \frac{1}{6x} \), which can be rewritten as \( y = -\frac{9}{8} + \frac{1}{6}x^{-1} \). Here, \( x \) is raised to the power of -1 (in the denominator), so it does not follow the form of a linear function.

Answer:

nonlinear