when a converting linear equation into an augmented matrix, which equation form is needed?
slope-intercept form
negative form
graph form
standard form
When converting a linear equation into an augmented matrix, the most useful form to start with is the standard form. A linear equation in two variables in standard form looks like this:
Ax + By = C
Where A, B, and C are constants, and x and y are the variables.
For a system of equations, each equation can be written in standard form. These equations can then be represented as an augmented matrix, where each row corresponds to an equation and each column (except for the last column) corresponds to a variable. The last column represents the constant terms.
For example, if you have a system of two equations:
1. 2x + 3y = 6
2. 4x - 5y = -2
The corresponding augmented matrix would be:
| 2 3 | 6 |
| 4 -5 | -2 |
In this matrix representation, the lines of the matrix represent the equations, the columns to the left of the vertical line represent the coefficients of the variables x and y respectively, and the column on the right of the vertical line represents the constants from the right-hand side of the equations.
This matrix can then be used for various matrix operations, such as Gaussian elimination, to solve the system of equations.