Questions: y+3=-(1/3)(2x+6)

y+3=-(1/3)(2x+6)
Transcript text: y+3=-\frac{1}{3}(2 x+6)
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Solution

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Solution Steps

Step 1: Expand the right-hand side

Start by expanding the right-hand side of the equation: \[ y + 3 = -\frac{1}{3}(2x + 6) \] Distribute \(-\frac{1}{3}\) to both terms inside the parentheses: \[ y + 3 = -\frac{1}{3} \cdot 2x - \frac{1}{3} \cdot 6 \] Simplify the multiplication: \[ y + 3 = -\frac{2}{3}x - 2 \]

Step 2: Move all terms to one side

To write the equation in standard form \(Ax + By + C = 0\), move all terms to one side: \[ y + 3 + \frac{2}{3}x + 2 = 0 \] Combine like terms: \[ \frac{2}{3}x + y + 5 = 0 \]

Step 3: Eliminate fractions

Multiply every term by 3 to eliminate the fraction: \[ 3 \cdot \frac{2}{3}x + 3 \cdot y + 3 \cdot 5 = 0 \] Simplify: \[ 2x + 3y + 15 = 0 \]

Final Answer

The equation in standard form is: \[ \boxed{2x + 3y + 15 = 0} \]

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