Write the equation in standard form. 2y + 3 = -1/3(x – 2)

To write the equation (2y + 3 = -frac{1}{3}(x – 2)) in standard form, we will follow these steps:

1. Distribute the (-frac{1}{3}) on the right side:

[

2y + 3 = -frac{1}{3}x + frac{2}{3}

]

2. Subtract 3 from both sides to isolate the (y) term:

[

2y = -frac{1}{3}x + frac{2}{3} – 3

]

Convert (3) to a fraction with a denominator of 3:

[

3 = frac{9}{3}

]

So, we have:

[

2y = -frac{1}{3}x + frac{2}{3} – frac{9}{3}

]

This simplifies to:

[

2y = -frac{1}{3}x – frac{7}{3}

]

3. Multiply the whole equation by 3 to eliminate the fractions:

[

3(2y) = 3left(-frac{1}{3}xright) – 3left(-frac{7