Q1B. - Algebra 1

Question

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

$y=x^2-4$

Step-by-Step Solution

Answer

The given equation $y=x^2-4$ is not a linear equation.

As, the given equation is not linear equation. Therefore, the given equation cannot be written in standard form of the linear equation.

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 width="14" height="19" style="max-width: none; vertical-align: -4px;" $C$ are integers with greatest common factor of 1.

 

The given equation is $y=x^2-4$.

 

As, the equation $y=x^2-4$ cannot be written in the form $Ax+By=C$ because in the given equation $y=x^2-4$, degree of $x$ is 2 while the degree of $x$ is 1 in the equation $Ax+By=C$.

 

Therefore, the given equation $y=x^2-4$ is not a linear equation.

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

As, the given equation is not linear equation. Therefore, the given equation cannot be written in standard form of the linear equation.