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

Verified step by step guidance

1. Rewrite the equation in slope-intercept form, \( y = mx + b \), if possible. In this case, solve for \( x \) to find the line's equation.
2. The equation \(-3x + 6 = 0\) can be rewritten as \(x = 2\). This represents a vertical line.
3. Identify the domain of the line. Since it's a vertical line, the domain is just the single value \(x = 2\).
4. Identify the range of the line. A vertical line extends infinitely in the vertical direction, so the range is all real numbers.
5. Graph the line by drawing a vertical line through \(x = 2\) on the coordinate plane.

Key Concepts

Linear Equations

A linear equation is an algebraic expression that represents a straight line when graphed on a coordinate plane. It typically takes the form y = mx + b, where m is the slope and b is the y-intercept. In the given equation, -3x + 6 = 0 can be rearranged to find the value of x, which represents a vertical line in this case.

Domain and Range

The domain of a function refers to all possible input values (x-values) that can be used in the function, while the range refers to all possible output values (y-values) that result from those inputs. For the equation -3x + 6 = 0, the domain is all real numbers since x can take any value, and the range is limited to the single value of y that corresponds to the solution of the equation.

Graphing Lines

Graphing a line involves plotting points that satisfy the equation and connecting them to form a straight line. For the equation -3x + 6 = 0, we can find the x-intercept by setting y to zero, which gives us a vertical line at x = 2. Understanding how to graph lines helps visualize the relationship between variables in linear equations.