Question

is the function $y = -\frac{7}{3} + \frac{x}{5}$ linear or nonlinear? linear nonlinear

Explanation:

Step1: Recall linear function form

A linear function is in the form \( y = mx + b \), where \( m \) (slope) and \( b \) (y - intercept) are constants, and the exponent of \( x \) is 1.

Step2: Rewrite given function

The given function is \( y = -\frac{7}{3}+\frac{x}{5} \). We can rewrite it as \( y=\frac{1}{5}x-\frac{7}{3} \). Here, \( m = \frac{1}{5} \) (a constant) and \( b=-\frac{7}{3} \) (a constant), and the exponent of \( x \) is 1. So it fits the form of a linear function.

Answer:

linear