The linear equation is: y= |x+6 |.
To identify the linear equation from the given options, we can analyze each equation:
A) y = x^6
b) y=x/6
c) y=6/x
d) y= |x+6 |
Since we are looking for a linear equation, we can eliminate the options that represent non-linear or non-linear relationships:
A) y = x^6 : This is a polynomial function of degree 6, which is not linear.
b) y=x/6: This is a rational function, which is not linear.
c) y=6/x: This is a rational function, which is not linear.
Only option d) y=∣x+6∣ remains as a possible linear equation.
To determine if this is indeed a linear equation, we can rewrite it as y=∣x∣+6, which has a constant term (6) and a linear coefficient (1) on the absolute value term.
This is a linear equation, so the correct answer is: