Graph each line. Give the domain and range. -3x + 6 = 0

Verified step by step guidance

1. Rewrite the given equation to isolate the variable y. Since the equation is -3x + 6 = 0 and does not contain y, recognize that this represents a vertical line where x is constant.
2. Solve for x by adding 3x to both sides: 6 = 3x, then divide both sides by 3 to get x = 2.
3. Understand that the graph of x = 2 is a vertical line crossing the x-axis at 2, and it extends infinitely in the y-direction.
4. Determine the domain: since x is always 2, the domain is the single value {2}.
5. Determine the range: because y can be any real number along the vertical line, 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 in the form Ax + By = C, you can find intercepts or rewrite the equation to identify the line's slope and position on the coordinate plane.

Domain of a Function

The domain is the set of all possible input values (x-values) for which the function or relation is defined. For most linear equations, the domain is all real numbers unless restricted by the equation or context.

Range of a Function

The range is the set of all possible output values (y-values) that the function can take. For linear equations, the range depends on the slope and orientation of the line; vertical or horizontal lines have specific ranges.