Question

Write the equation in standard form. 4y−5x=3(4x−2y+1)

Answer 1

To write the equation in standard form, we need to isolate the variables on one side of the equation and the constants on the other side. We can do this by combining like terms and using the distributive property.

First, we distribute the 3 on the right side of the equation:

4y - 5x = 12x - 6y + 3

Then, we combine like terms:

4y - 5x = 12x - 6y + 3

= -x + 6y + 3

Finally, we move all the constants to the right side of the equation and all the variables to the left side:

x - 6y = -3

This is the standard form of the equation. In standard form, the equation has the form ax + by = c, where a and b are coefficients, and c is a constant. In this case, the coefficients are 1 and -6, and the constant is -3.

Answer 2

17x - 10y = - 3

Explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

4y - 5x = 3(4x - 2y + 1) ← distribute parenthesis

4y - 5x = 12x - 6y + 3 ( subtract 4y - 5x from both sides )

0 = 17x - 10y + 3 ( subtract 3 from both sides )

- 3 = 17x - 10y , that is

17x - 10y = - 3 ← in standard form