Question

y + 9 = \frac{1}{3}(x - 2)

Explanation:

Step1: Multiply both sides by 3

To eliminate the fraction, we multiply each side of the equation \( y + 9=\frac{1}{3}(x - 2) \) by 3. This gives us \( 3(y + 9)=x - 2 \).

Step2: Distribute the 3

Using the distributive property \( a(b + c)=ab+ac \), we expand the left - hand side: \( 3y+27=x - 2 \).

Step3: Solve for x (if we want to express x in terms of y)

We add 2 to both sides of the equation \( 3y + 27=x-2 \). So, \( x=3y + 27+2=3y+29 \).
Or if we want to solve for y (assuming it's a linear equation in two variables and we solve for y):

Step2 (alternative, solving for y): Subtract 9 from both sides

Starting from \( y + 9=\frac{1}{3}(x - 2) \), subtract 9 from both sides: \( y=\frac{1}{3}(x - 2)-9 \).

Step3 (alternative): Distribute and simplify

Distribute the \(\frac{1}{3}\): \( y=\frac{1}{3}x-\frac{2}{3}-9 \). Then, combine the constant terms. Since \( 9=\frac{27}{3} \), we have \( y=\frac{1}{3}x-\frac{2}{3}-\frac{27}{3}=\frac{1}{3}x-\frac{29}{3} \).

If we assume it's a typo and the equation is \( y + 9=\frac{1}{3}(x - 2) \) and we want to write it in standard form \( Ax+By = C\):
From \( 3(y + 9)=x - 2 \), we have \( 3y+27=x - 2 \). Then, move all terms to one side: \( -x+3y=-2 - 27 \), so \( -x + 3y=-29 \) or multiply both sides by - 1 to get \( x-3y = 29 \).

Answer:

If solving for \( x \) in terms of \( y \): \( x = 3y+29 \)
If solving for \( y \) in terms of \( x \): \( y=\frac{1}{3}x-\frac{29}{3} \)
In standard form (\( Ax + By=C \)): \( x-3y = 29 \)