Question

Determine whether each equation is a linear equation. Write yes or no. If yes, write the equation in standard form.

$x^2+3y=8$

Short answer

No, the equation is not a linear equation.

Step-by-step solution

Step 1. State the concept of standard form of linear equation.

Alinear equationis anyequationthat can be written in the form $ax+by=0$, where a and b are real numbers and x is a variable. This form is sometimes called the standard form of a linear equation.

No variable in alinear equationis raised to a power greater than 1. Linear equationsare those equations that are of the first order.

Standard form of Linear Equation is $Ax+By+C=0$, where A, B and C are any integer.

Step 2. Rewrite the equation in standard form.

In order to rewrite the equation$x^2+3y=8$in standard form subtract 8 from both sides as follows:

$$\begin{gathered} x^2+3y=8 \\ {x}^2+3y-8=8-8 \\ {x}^2+3y-8=0 \end{gathered}$$

Step 3. State the Conclusion.

The equation is not in standard form because x is not a linear. Since the variables in the equation has the highest exponent as 2, so the equation is not linear.