Question

Which of the following is correctly written in Standard Form?

4x - 3y = 6

-4x + 2y = 8

y = 4/5x + 4

4/5x + 2y = 6

Answer 1

Standard form for a linear equation is Ax + By = C with A, B, C integers, A ≥ 0, and usually with no common factor > 1.

Check each:
- 4x − 3y = 6 — yes: A = 4 (positive), coefficients are integers and relatively prime. (Correct)
- −4x + 2y = 8 — no: A is negative and all terms share a factor 2 (can be simplified/rearranged).
- y = (4/5)x + 4 — no: slope‑intercept form and has a fractional coefficient (can be converted to integer coefficients).
- (4/5)x + 2y = 6 — no: fractional coefficient (can be cleared by multiplying by 5 and simplified).

So only 4x − 3y = 6 is correctly in standard form as written.