91Ó°ÊÓ

When given a linear equation like \( -x + 5 = 0 \), the first step is to solve for the variable \(x\). This is essential to find where the line intersects the x-axis. Let’s go through the steps:
- Start with the equation: \(-x + 5 = 0\)
- Subtract 5 from both sides to isolate the term with \(x\): \(-x = -5\)
- Multiply both sides by \(-1\) to solve for \(x\): \(x = 5\)
This tells us that the line intersects the x-axis at \(x = 5\).

Simplifying the equation step by step helps ensure you do not make mistakes along the way. Once solved, it becomes much easier to graph the equation correctly.

A vertical line is unique in that it does not have a slope like other lines. The equation \(x = 5\) describes a vertical line where every point on the line has an x-coordinate of 5.
- It is of the form \(x = a\), where \(a\) is a constant.

To graph a vertical line, simply find the point on the x-axis that matches the constant (in this case, 5) and draw a straight vertical line through it. The y-coordinates can be any value.
Vertical lines are quite straightforward because they don’t slant; they go straight up and down, making them easy to identify and graph.

The domain and range of a function describe the set of possible input and output values, respectively.
- **Domain:** For our vertical line \(x = 5\), the domain is very specific. It consists of only one value, which is 5. This makes the domain \([5]\), indicating there is no other x-value for this line.
- **Range:** Unlike the domain, the range of a vertical line is all-encompassing in the y-direction. It includes all real numbers, represented as \( (-\forall,\forall) \). This is because the line extends infinitely up and down with every possible y-value.

Understanding the domain and range helps clarify where the line exists on the graph and can assist in solving more complex problems in the future.

In summary, the simplest ways to remember: Vertical lines have a domain consisting only of one number, but their range includes all real numbers.