In the previous section, we found several solutions to the equation 3x+2y=6. They are listed in (Figure). So, the ordered pairs \left(0,3\right), \left(2,0\right), and \left(1,\frac{3}{2}\right) are some solutions to the equation 3x+2y=6. We can plot these solutions in the rectangular coordinate system as shown in (Figure).

3x+2y=6

x y \left(x,y\right)

0 3 \left(0,3\right)

2 0 \left(2,0\right)

1 \frac{3}{2} \left(1,\frac{3}{2}\right)

The figure shows four points on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. Dots mark off the four points at (0, 3), (1, three halves), (2, 0), and (4, negative 3). The four points appear to line up along a straight line.