Question

Write y = – two-thirds x + 7 in standard form using integers.

A. 2x + 3y = 21
B. 3x – 2y = 21
C. –2x – 3y = 21
D. –2x + 3y = 7

Answer 1

The standard form of y =
`-(2)/(3)` x + 7 is 2x + 3y = 21 ⇒ A

Explanation:

The standard form of the linear equation is ax + by = c, where a, b, and c are integers

∵ y =
`-(2)/(3)` x + 7

→ Multiply each term by 3 to cancel the denominator

∴ 3(y) = 3(
`-(2)/(3)`) x + 3(7)

∴ 3y = -2x + 21

→ Add 2x to both sides to move x from the right side to the left side

∵ 2x + 3y = -2x + 2x + 21

∴ 2x + 3y = 21

∴ The standard form of y =
`-(2)/(3)` x + 7 is 2x + 3y = 21