Given equation of the line is 3x + 2y = 2.
x/2 + y/2 = 1
This equation is of the form x/a + y/b = 1, with a = 2/3, b = 1.
The line 3x + 2y = 2 intersects the X-axis at A( , 0) and Y-axis at B(0, 1).
Required line is passing through the midpoint of AB
Midpoint of AB = \((\frac {\frac{2}{3}+0}{2}, \frac {0+1} {2}) = (\frac {1}{3}, \frac {1}{2})\)
∴ Required line passes through (0, 0) and \( (\frac {1}{3}, \frac {1}{2})\).
Equation of the line in two point form is \(\frac {y-y_1}{y_2-y_1} =\frac{x-x_1}{x_2-x_1}\)
2y = 3x
∴ 3x – 2y = 0
