Question

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

$-4y+6=2$

Short answer

Yes, the given equation$-4y+6=2$ is a linear equation and the given equation$-4y+6=2$ in standard form is $y=1$.

Step-by-step solution

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 $-4y+6=2$.

The given equation can be written as:

$$\begin{gathered} -4y+6=2 \\ -4y=2-6 \\ -4y=-4 \\ y=\frac{-4}{-4} \\ y=1 \end{gathered}$$

Therefore, by comparing the given equation $y=1$with the equation $Ax+By=C$, it can be noticed that: $A=0,B=1$and $C=1$.

As, the equation$-4y+6=2$ can be written in the form $Ax+By=C$.

Therefore, yes, the given equation$-4y+6=2$is a linear equation.

Step 2. Write the given equation in standard form.

The given equation is $-4y+6=2$.

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

The given equation in standard form is $y=1$.

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