Final answer:
To convert line equations to standard form, terms involving variables are placed on one side and constants on the other. Equations (a) y = 6x - 4, (c) y = 4 - 6x, and (d) 4 - 6x = y are rearranged to their respective standard forms -6x + y = -4, 6x + y = 4, and 6x - y = 4. Equation (b) 6x - y = 4 is already in standard form.
Step-by-step explanation:
The student has asked to convert the line equations to standard form.
Starting with equation (a) y = 6x - 4, we move all terms involving variables to one side of the equation and constants to the other side to get the standard form, which is Ax + By = C. Subtracting 6x from both sides gives us -6x + y = -4, which is the standard form. Notice that it is okay to have negative coefficients in the standard form.
Equation (b) 6x - y = 4 is already in standard form, as the variables and constants are on opposite sides and the coefficients are integers.
For equation (c) y = 4 - 6x, arranging it similarly by adding 6x to both sides while keeping y on the left side leads us to 6x + y = 4, this is the standard form.
Lastly, equation (d) 4 - 6x = y can be rearranged by subtracting y from both sides and adding 6x to both sides to obtain 6x - y = 4, and this, too, is in standard form.
In conclusion, all equations can be expressed in standard form by appropriately rearranging terms and ensuring that all variable terms are on one side and the constant on the other.