To graph the line defined by the equation [tex]\(-2x = -8\)[/tex], let's solve it step-by-step:
1. Isolate the Variable [tex]\(x\)[/tex]:
The goal is to find the value of [tex]\(x\)[/tex] that satisfies the equation.
[tex]\[
-2x = -8
\][/tex]
To isolate [tex]\(x\)[/tex], we need to divide both sides by [tex]\(-2\)[/tex]:
[tex]\[
x = \frac{-8}{-2}
\][/tex]
This simplifies to:
[tex]\[
x = 4
\][/tex]
2. Understand the Nature of the Line:
The equation [tex]\(-2x = -8\)[/tex] simplifies to [tex]\(x = 4\)[/tex]. This indicates that [tex]\(x\)[/tex] is always 4, regardless of the value of [tex]\(y\)[/tex].
This means the line is vertical and crosses the x-axis at [tex]\(x = 4\)[/tex].
3. Graph the Line:
- On a coordinate plane, locate the point where [tex]\(x = 4\)[/tex] on the x-axis.
- Draw a vertical line passing through [tex]\(x = 4\)[/tex].
### Graph Representation:
- The vertical line would look something like this:
[tex]\[
\begin{array}{ccccc}
& & | & & \\
& & | & & \\
& & | & & \\
& & | & & \\
--+--+--+--+---
& & | & & \\
\cdots & & \mathbf{(4,0)} & & \cdots \\
& & | & & \\
& & | & & \\
& & | & & \\
\end{array}
\][/tex]
- The line passes through [tex]\((4, y)\)[/tex] for all values of [tex]\(y\)[/tex].
This is the graph of the equation [tex]\(-2x = -8\)[/tex], which is a vertical line through [tex]\(x = 4\)[/tex].
