Question

Write y- 2/3 = 4/3 (x+2) in standard form

Answer 1

The equation y - 2/3 = 4/3 (x + 2) is rewritten in standard form by first multiplying by 3 to remove fractions, distributing and combining like terms, and then rearranging the equation to -4x + 3y = 10.

Step-by-step explanation:

To write the equation y - ⅓ = ⅔ (x + 2) in standard form, we should begin by eliminating the fractions and getting the x and y terms on one side of the equation and the constant on the other. We will use the following steps:

1. Multiply both sides by 3 to eliminate the fraction on the left side: 3(y - ⅓) = 3(⅔ (x + 2)).
2. This simplifies to: 3y - 2 = 4(x + 2).
3. Distribute the 4 on the right side: 3y - 2 = 4x + 8.
4. Add 2 to both sides to move the constant to the right side: 3y = 4x + 10.
5. Finally, to get the standard form, which is Ax + By = C, subtract 4x from both sides: -4x + 3y = 10.

This is the standard form of the equation Ax + By = C, where A = -4, B = 3, and C = 10.