Find the equation of the line which has Y-intercept 4 &is parallel to line 2x-3y=7.Find the co-ordinates of the point where it cuts X-axis.

The equation of a line with a y-intercept of c and a slope
of m is given as y=mx + c.

The line we have to determine is
parallel to the line 2x - 3y = 7. This is possible if they have the same
slope.

2x - 3y = 7

=>
3y = 2x - 7

=> y = (2/3)x -
(7/3)

The slope of the line we have to determine is (2/3).
Its y-intercept is 4, this gives the equation of the line
as

y = (2/3)x + 4

=> 3y
= 2x + 12

=> 2x - 3y + 12 =
0

Where the line intersects the x-axis y =
0

=> 2x = -12

=>
x = -6

The coordinates of the point where it intersect the
x- axis is (-6 , 0)

The required equation of
the line is 2x - 3y + 12 = 0 and the coordinates of the point where it intersects the
x-axis are (-6 , 0)