Question

Determine whether each equation is a linear equation. Write the equation in standard form.

$\frac{1}{3}y=-1$

Short answer

The given equation$\frac{1}{3}y=-1$ is a linear equation.

The given equation$\frac{1}{3}y=-1$ in standard form is $y=-3$.

Step-by-step solution

Part a. Step 1. Determine whether the given equation is a linear equation.

A linear equation is an equation that forms a line when it is graphed. Linear equations are written in the form $Ax+By=C$, where$A$ and$B$ are not both zero and $A$,$B$ and$C$ are integers with greatest common factor of 1.

The given equation is $\frac{1}{3}y=-1$.

The given equation can be written as:

$\begin{array}{c}\frac{1}{3}y=-1\\ y=-3\end{array}$

Therefore, by comparing the given equation$y=-3$ with the equation $Ax+By=C$, it can be noticed that:

$A=0$,$B=1$ and $C=-3$.

As, the equation$\frac{1}{3}y=-1$ can be written in the form $Ax+By=C$.

Therefore, the given equation$\frac{1}{3}y=-1$ is a linear equation.

Part a. Step 2. Write the given equation in standard form.

The given equation is $\frac{1}{3}y=-1$.

The standard form of the linear equation is $Ax+By=C$.

The given equation in standard form is:

$y=-3$

Where $A=0$,$B=1$ and $C=-3$.