How to graph 3y +2x =-12

To graph the equation 3y + 2x = -12, we can rearrange the equation to solve for y and then create a table of values or plot the intercepts.

1. Rearrange the equation to solve for y:
3y = -2x - 12
Divide both sides by 3:
y = (-2/3)x - 4

2. Create a table of values:
Choose values for x and calculate corresponding values for y.
Let's choose x = -3, -2, 0, 2, and 3.
For x = -3, y = (-2/3)(-3) - 4 = 2 - 4 = -2
For x = -2, y = (-2/3)(-2) - 4 = 4/3 - 4 = -8/3
For x = 0, y = (-2/3)(0) - 4 = -4
For x = 2, y = (-2/3)(2) - 4 = -4/3 - 4 = -16/3
For x = 3, y = (-2/3)(3) - 4 = -2 - 4 = -6

3. Plot the points on a graph:
Plot the points (-3,-2), (-2, -8/3), (0, -4), (2, -16/3), and (3, -6) on a coordinate plane.

4. Connect the points:
Graph a line that passes through the points you plotted.

The final graph will appear as a straight line with a negative slope passing through the points on the coordinate plane.