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
-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 - 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