1. Find the Slope of the Given Line
* Rewrite the equation in slope-intercept form (y = mx + b), where 'm' is the slope:
3y = -2x + 12
y = (-2/3)x + 4
* The slope of the given line is -2/3.
2. Parallel Lines Have the Same Slope
* Any line parallel to the given line will also have a slope of -2/3.
3. Choose an Equation with the Same Slope
* There are infinitely many lines with a slope of -2/3. Here's one example:
y = (-2/3)x + 5
* You can create other parallel lines by changing the y-intercept (the 'b' value).
Therefore, the equation y = (-2/3)x + 5 represents a line that is parallel to 2x + 3y = 12.
