Answer
A) $y=-\frac{2}{3}x+4$
Work Step by Step
Step 1: State Equation; $2x+3y=12$
Step 2: Isolate variable that is to be found; subtract other values on the side containing the variable; $2x + 3y (-2x) = 12 (-2x)$.
Step 3: Clean up equation; organize values; $3y = -2x + 12$
Step 4: Eliminate the coefficient of the variable to get the value for just 1 of the variable (basic value of variable); $3y\div(3)=(-2x+12)\div(3)$
Step 5: Clean up equation; organize values; $y=-\frac{2}{3}x + 4$
Step 6: State final answer and add appropriate units if any; $y=-\frac{2}{3}x+4$
Explanation: You must isolate the variable to be found because you want to get to the point where there is only one base value of 1 quantity of that variable to build up upon for other q=equations. By doing steps 1 - 5, you have made sure the $y$ is only on one side, and then made sure that there was only one quantity of it; the base value of $y$. After doing that, the equation is done; $y$ has been given a value of $x$ and a constant. If the equation had an exponent or other factors, you may have had to do some other arithmetic functions to eliminate those values; the main point would be to just get down to the basic value of just one y. Therefore, the final answer here is $y=-\frac{2}{3}x + 4$.
