Given line: 2x – 3y – 7 = 0

Its slope is,

3y = 2x – 7

y = (2/3) x – 7/3

⇒ m = 2/3

So, the equation of the line parallel to the given line will be 2/3

Also given, the y-intercept is 4 = c

Hence, the equation of the line is given by

y = mx + c

y = (2/3) x + 4

3y = 2x + 12

2x – 3y + 12 = 0

Now, when this line intersects the x-axis the y co-ordinate becomes zero.

So, putting y = 0 in the line equation, we get

2x – 3(0) + 12 = 0

2x + 12 = 0

x = -12/2 = 6

Hence, the co-ordinates of the point where it cuts the x-axis is (-6, 0).