4x+2y=7
Solve for y
2y=-4x+7
Divide through by 2
y=-2x+7/2
The slope is m=-2 from comparing it to y=mx+b
Parallel lines slope the same way so their slopes are equal
Use formula
y-y1 = m(x - x1) with m = -2, and (x,y) = (1,0)
y-0 = -2(x - 1)
y = -2x + 2

But the easiest way to get an equation of a line parallel to another line which
you have the equation of and a point it must pass through for, is to solve for
the constant term, substitute the point in the other side and replace the
constant term with what you get.

That's because the equations of any two parallel line can be the same except for
the constant terms. Therefore:

 4x+2y=7  The constant term is already solved for.

Substitute (x,y) = (1,0) on the left side
 
4x + 2y = ?
4(1) + 2(0) = 4 + 0 = 4

So replace the constant term 7 by 4

4x + 2y = 4

That's an answer.  But you can simplify it! 
Divide through by 2 and get

2x + y = 2

or

y = -2x + 2

Edwin