Question

which equation is non - linear?
a. $y = \frac{1}{x}+3$

b. $y = 4x - 5$

c. $y = \frac{x}{2}+6$

d. $y = x + x + 3$

Explanation:

Step1: Recall linear equation form

A linear equation in two variables is of the form \( y = mx + b \), where \( m \) and \( b \) are constants, and the exponent of \( x \) is 1.

Step2: Analyze Option A

For \( y=\frac{1}{x}+3 \), we can rewrite it as \( y = x^{-1}+3 \). Here, the exponent of \( x \) is - 1, not 1. So, it does not follow the linear equation form.

Step3: Analyze Option B

For \( y = 4x-5 \), it is in the form \( y=mx + b \) with \( m = 4 \) and \( b=-5 \). So, it is a linear equation.

Step4: Analyze Option C

For \( y=\frac{x}{2}+6 \), we can rewrite it as \( y=\frac{1}{2}x + 6 \), which is in the form \( y = mx + b \) with \( m=\frac{1}{2}\) and \( b = 6 \). So, it is a linear equation.

Step5: Analyze Option D

For \( y=x + x+3 \), we can simplify it to \( y = 2x+3 \), which is in the form \( y=mx + b \) with \( m = 2 \) and \( b = 3 \). So, it is a linear equation.

Answer:

A. \( y=\frac{1}{x}+3 \)