Standard form looks like this:
ax + by = c
Where a, b, and c are all integers; a ≥ 0; and there is no common factor of a, b, and c (except 1).
First, add (2/7)x to both sides:
(2/7)x + y = -3
Multiply by the denominator of the coefficient of x:
2x + 7y = -21
Now, a, b, and c are all integers; a ≥ 0; and there are no common factors (other than 1) of a, b, and c.
Mission accomplished! By the way, you can graph both equations using the Desmos online graphing calculator to verify that they are "one and the same" line.
PS: If either a, b, or c is irrational, then it may not be possible to convert to integer coefficients and an integer constant. But as long as a, b, and c are rational numbers, you can always convert a slope-intercept linear equation into a standard form equation.
Note that the required conditions make the standard form of a linear equation unique.
