Question

is the function $y = \frac{2}{3}\sqrt{x} + \frac{6}{7}$ 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).

Step2: Analyze the given function

The given function is \( y=\frac{2}{3}\sqrt{x}+\frac{6}{7} \), which can be rewritten as \( y = \frac{2}{3}x^{\frac{1}{2}}+\frac{6}{7} \). Here, the exponent of \( x \) is \( \frac{1}{2} \), not 1. So it does not match the linear function form.

Answer:

nonlinear