write an equation of the line parallel to the line 2x-3y-3=0

and having the same x-intercept as the line 4x-7y-14=0

First, we need the slope of line 1

2x-3y-3=0

-3y = -2x + 3

y = 2/3 x - 1

The slope is 2/3

Next, we need the value of x where the second line crosses

the x axis. The value of y at that point is zero.

4x-7y-14=0

4x - 7(0) - 14 = 0

4x = 14

x = 14/4

x = 7/2

Finally, we use the point (7/2, 0) to find the y-intercept

of the line we are looking for.

y = mx + b

y - mx = b

b = y - mx

Plug in the x and y values of the x-intercept.

b = 0 - (2/3 * 7/2)

b = - (14/6)

b = -7/3

Our equation is y = 2/3 x - 7/3