Question

How would you graph the line $2x + 8 = 0$?

Answer 1

Hint: First step is to isolate the variable terms on one side by performing the same mathematical operations on both sides of the equation. Next step is to isolate the constant terms on the other side by performing the same mathematical operations on both sides of the equation. Next step is to make the coefficient of the variable equal to $1$ using multiplication or division property. Next, draw graph AB of a line parallel to Y-axis at a distance of 4 units from Y-axis in the negative direction of X-axis.

Complete step by step answer:
The algebraic equation is $2x + 8 = 0$.
We have to find the value of $x$.
First step is to isolate the variable terms on one side by performing the same mathematical operations on both sides of the equation.
Here, the variable term $x$ is already on one side of the equation.
Thus, $2x + 8 = 0$.
Next step is to isolate the constant terms on the other side by performing the same mathematical operations on both sides of the equation.
So, subtracting $8$ from both sides of the equation $2x + 8 = 0$.
$ \Rightarrow 2x + 8 - 8 = 0 - 8$
It can be written as
$ \Rightarrow 2x = - 8$
Next step is to make the coefficient of the variable equal to $1$ using multiplication or division property.
So, divide both sides of the equation by $2$, we get
$ \Rightarrow \dfrac{{2x}}{2} = \dfrac{{ - 8}}{2}$
Cancel the common factor.
$\therefore x = - 4$
If it is treated as an equation in two variables, then it can be written as $1 \cdot x + 0 \cdot y + 4 = 0$ and it is represented by a line.
Here, all the values of $y$ are permissible, because $0 \cdot y$ is always $0$. However, $x$ must satisfy the equation $2x + 8 = 0$.

The graph AB is a line parallel to Y-axis at a distance of 4 units from Y-axis in the negative direction of X-axis.

Hence, the straight line, so obtained is the required graph of given linear equation.

Note: If $a > 0$, then $x = a$ represent the equation of a line parallel to Y-axis in the positive direction of X-axis and $x = - a$ in the negative direction of X-axis.