Understanding Standard Form of a Linear Equation
To express the equation y = 2 in standard form, we need to rewrite it in the format Ax + By = C, where A, B, and C are integers, and A should be non-negative.
Step-by-Step Conversion
- Identify the Given Equation:
The original equation is y = 2.
- Rearranging the Equation:
We want to include the variable x in the equation. To do this, we can add 0x to the equation since adding zero does not change its value.
So, we rewrite it as:
0x + y = 2.
- Standard Form Structure:
Now, the equation is in the format Ax + By = C. Here:
- A = 0
- B = 1
- C = 2
- Final Standard Form:
Thus, the standard form of the equation y = 2 is:
0x + 1y = 2.
Important Points to Note
- Linear Equation:
The equation represents a horizontal line on a graph where y is always 2, regardless of the value of x.
- Graphical Representation:
This line will intersect the y-axis at (0, 2) and will be parallel to the x-axis.
- Interpreting Variables:
In the context of this equation, x can take any value, but y remains constant at 2.
This transformation illustrates how to convert a simple linear equation into standard form while maintaining its integrity in representation.