The equation of a line can often be expressed in standard form as Ax + By = C, where A, B, and C are integers, and A should be non-negative. Let’s analyze the equation you’ve given: 2x + 3y = 6.
To clarify further, the standard form of the line can be derived and rearranged to express it clearly:
1. Start with the original equation:
2x + 3y = 62. Solve for y to understand its slope and intercept better. Subtract 2x from both sides:
3y = -2x + 63. Next, divide every term by 3 to get y by itself:
y = - rac{2}{3}x + 2This form, y = mx + b, where m is the slope and b is the y-intercept, indicates that the slope of the line is - rac{2}{3} and it crosses the y-axis at (0, 2).
To recap, the given equation of the line is already presented in standard form, 2x + 3y = 6, which is acceptable as it maintains the required format of integers along with A being non-negative. This simplicity makes it easy to work with in many contexts, such as graphing or solving systems of equations.
In summary, the line represented by the formula you provided is expressible in standard form as 2x + 3y = 6, where you can see clearly that this meets all the conditions for the standard form of a linear equation.