\( 2 x+3 y=12 \), solve for \( y \)

To solve for \( y \) in the equation \( 2x + 3y = 12 \), first isolate the term involving \( y \). Start by subtracting \( 2x \) from both sides: \[ 3y = 12 - 2x \] Next, divide every term by 3 to solve for \( y \): \[ y = \frac{12 - 2x}{3} \] So, \( y = 4 - \frac{2}{3}x \). There you go—now you have \( y \) expressed in terms of \( x \)! Switching gears, did you know that this kind of equation represents a straight line on a graph? The coefficients for \( x \) and \( y \) show us how steep the line is, and the constant term represents where it crosses the y-axis. It's like drawing a picture with numbers, where context matters! If you're ever solving these systems of equations, remember to always double-check whether your isolations might have switched signs! Also, be cautious with the coefficients — one tiny slip can lead to a world of confusion in your final answer. Keep it neat, and it’ll be a breeze!