Graph each line. Give the domain and range. -x + 5 = 0

Verified step by step guidance

1. Rewrite the given equation \(-x + 5 = 0\) to isolate \(x\). Add \(x\) to both sides to get \(5 = x\), or equivalently \(x = 5\).
2. Recognize that the equation \(x = 5\) represents a vertical line on the coordinate plane where \(x\) is always 5 regardless of \(y\).
3. To graph this line, draw a straight vertical line passing through all points where the \(x\)-coordinate is 5.
4. Determine the domain of the line: since \(x\) is fixed at 5, the domain is the single value \(\{5\}\).
5. Determine the range of the line: because \(y\) can be any real number, the range is all real numbers, expressed as \(( -\infty, \infty )\).

Key Concepts

Graphing Linear Equations

Graphing a linear equation involves plotting all points (x, y) that satisfy the equation. For equations like -x + 5 = 0, which can be rewritten as x = 5, the graph is a vertical line crossing the x-axis at 5. Understanding how to interpret and plot such lines is essential for visualizing solutions.

Domain of a Function or Relation

The domain is the set of all possible input values (x-values) for which the equation or function is defined. For a vertical line like x = 5, the domain is a single value, x = 5, since the line exists only at that x-coordinate.

Range of a Function or Relation

The range is the set of all possible output values (y-values) that the equation or function can take. For the vertical line x = 5, the range includes all real numbers because y can be any value along that vertical line.