Given the equation:
[tex](-10+y^2)-y^2=-7x+10[/tex]
To determine if the equation is a linear equation, the first step is to simplify it. To do so, erase the parentheses and simplify the like terms:
[tex]\begin{gathered} (-10+y^2)-y^2=7x+10 \\ -10+y^2-y^2=7x+10 \\ -10+0y^2=7x+10 \\ -10+0y=7x+10 \end{gathered}[/tex]
The terms "+y²" and "-y²" canceled each other, this is why the variable y is multiplied by zero. Then the only variable left is "x", which suggests that the equation represents a vertical line.
To write this equation in standard form, you have to pass the x-term to the left side of the equation and the constant to the right side of it:
[tex]\begin{gathered} -10+0y=-7x+10\text{ \rightarrow add 10 to both sides of the equation} \\ -10+10+0y=-7x+10+10 \\ 0y=-7x+20\text{ \rightarrow add 7x to both sides of the equation} \\ 0y+7x=-7x+7x+20 \\ 0y+7x=20 \\ 7x+0y=20 \end{gathered}[/tex]
The line written in standard form is 7x+0y=20.
Vertical lines are considered to be linear equations.
