Q. 17 - Algebra 2

Question

State whether each equation or function is linear. Write yes or no. If
 no, explain your reasoning.

$3x^2-y=6$

Step-by-Step Solution

Answer

No, the equation is not linear. It is not of the form $y=mx+b$.

Step 1. Defining the linear equation

By definition, we have that a linear equation is of the form $y=mx+b$.

Step 2. Simplifying the given equation

We have:

$\begin{array}{l}3x^2-y=6\\ y=3x^2-6\\ y=a{x}^2+bx+c\end{array}$

Step 3. Determining the final equation

The given equation is not a linear equation; it is not of the form $y=mx+b$. It is a quadratic equation.