SOLUTION: Find the equation passing through (1,0) and that is parallel to 4x+2y=7.

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Question 1206663: Find the equation passing through (1,0) and that is parallel to 4x+2y=7.
Found 2 solutions by Edwin McCravy, math_tutor2020:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
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 

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

The slope of Ax+By = C is m = -A/B
If B = 0, then the slope is undefined and the line is vertical.

In the case of 4x+2y = 7 the slope is m = -A/B = -4/2 = -2.

Any parallel line to this will also have slope of -2.
Parallel lines have equal slopes but different y intercepts.

y = mx+b
y = -2x+b .... plug in slope
0 = -2*1+b .... plug in point's coordinates
0 = -2+b
b = 2

We determine that
m = -2 and b = 2
It means y = mx+b turns into y = -2x+2
That is the slope-intercept version of the answer.

If you want the answer in standard form, then add the 2x to both sides
y = -2x+2
2x+y = 2
Note that doubling both sides leads to 4x+2y = 4, where we see the "4x+2y" expression show up again.
4x+2y = 7 is parallel to 4x+2y = 4
This is because Ax+By = C is parallel to Ax+By = D, where C+%3C%3E+D