The graph of a linear equation in one variable is a straight line that is either parallel to the x-axis or y-axis.
Understanding Linear Equations in One Variable
A linear equation in one variable is an equation that can be written in the form ax + b = 0 or ay + b = 0, where a and b are constants and x or y is the variable. The solutions to these equations are represented graphically as straight lines on the coordinate plane.
Graphical Representation
The key aspect to remember is that the graph's orientation depends on which variable is present in the equation. According to the provided reference:
- Equation in x: If the equation only contains x (e.g., x = c, where c is a constant), the graph is a vertical line parallel to the y-axis. All points on this line have the same x-coordinate (c), regardless of their y-coordinate.
- Equation in y: If the equation only contains y (e.g., y = c, where c is a constant), the graph is a horizontal line parallel to the x-axis. All points on this line have the same y-coordinate (c), regardless of their x-coordinate.
Examples
Let's consider a few examples to illustrate this concept:
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Example 1: x = 3
This is a linear equation in one variable (x). Its graph is a vertical line that passes through the point (3, 0) on the x-axis. Every point on this line has an x-coordinate of 3.
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Example 2: y = -2
This is a linear equation in one variable (y). Its graph is a horizontal line that passes through the point (0, -2) on the y-axis. Every point on this line has a y-coordinate of -2.
Summary
| Equation Form | Graph | Orientation |
|---|---|---|
| x = c | Vertical straight line | Parallel to y-axis |
| y = c | Horizontal straight line | Parallel to x-axis |
