Question

graph the given line. give the domain and range.\\(-x + 2 = 0\\)\\(\\)\\(\\)use the graphing tool to graph the line.

Explanation:

Step1: Solve the equation for x

We start with the equation \(-x + 2 = 0\). To solve for \(x\), we can add \(x\) to both sides and then subtract 0 from both sides (or more simply, isolate \(x\)).
Adding \(x\) to both sides gives \(2=x\), or \(x = 2\).

Step2: Analyze the graph of the line

The equation \(x = 2\) represents a vertical line. A vertical line has an undefined slope and is parallel to the \(y\)-axis. For a vertical line \(x = a\) (in this case \(a = 2\)):

• Domain: The domain is the set of all \(x\)-values that the line covers. Since the line is \(x = 2\), the only \(x\)-value is \(2\). So the domain is \(\{2\}\) (or in interval notation, \([2, 2]\)).
• Range: The range is the set of all \(y\)-values that the line covers. A vertical line extends infinitely in the positive and negative \(y\)-directions, so the range includes all real numbers. In interval notation, the range is \((-\infty, \infty)\).

Answer:

The equation \(-x + 2 = 0\) simplifies to \(x = 2\), which is a vertical line.

• Domain: \(\{2\}\) (or \([2, 2]\) in interval notation)
• Range: \((-\infty, \infty)\) (all real numbers)