Final answer:
To write the equation x - y = -3 in standard form, you rewrite it as -x + y = 3 after multiplying the entire equation by -1. However, if 'a' in standard form must be positive, the equation remains as x - y = -3.
Step-by-step explanation:
To rewrite the equation x - y = -3 in standard form, we need the x and y terms to be on the same side and the equation should be ax + by = c, where a, b, and c are integers and a is non-negative. Starting with the original equation:
x - y = -3
We rearrange it to the standard form:
-y = -x - 3
y = x + 3 (We multiplied the entire equation by -1 to get this step)
So, the proper standard form is: -x + y = 3
Now, check that the coefficients meet the standard form criteria:
a (the coefficient of x) is -1, which is acceptable.
b (the coefficient of y) is 1, and it is already positive.
c (the constant term) is 3.
Note that some textbooks require that the a coefficient in the standard form should be positive. If that was the requirement, we would not multiply by -1 in the final step, and our standard form would be instead x - y = -3.