Question

Fill in the missing values to write the equation of the line, in STANDARD FORM, using the given information.

y=2/3x−1

Answer 1

The equation of the line is:

`\[2x - 3y = 3\]`

Step-by-step explanation:

The given equation is
`\(y = (2)/(3)x - 1\)`. To convert it to standard form
`(\(Ax + By = C\)),`we need to eliminate fractions and rearrange the terms. First, multiply both sides by 3 to get rid of the fraction in the equation:
`\(3y = 2x - 3\).` Next, move all terms to one side of the equation to achieve the standard form:
`\(2x - 3y = 3\).`

In standard form, the coefficients A, B, and C must be integers, and A should be positive. In our final answer,
`\(2x - 3y = 3\)`, A is 2, B is -3, and C is 3, satisfying the requirements for standard form. This form is preferred in many mathematical contexts as it simplifies comparisons and calculations, making it a more convenient representation for the given equation.