Question 45752
Parallel lines will have the same slope. 
Slope intercept form is 
y = mx + c
where m is the slope and c is the y-intercept of the line

The line that satisfies the given equation:
x – 2y = 6
can be written as
y = x/2 - 3

Slope = 1/2

A line parallel to this line will also have slope = 1/2
Let us assume the equation of the line is 
y = mx + c
Now we know m = 1/2 from above, also given that (1,4) is a point on the line so it satisfies the equation of the line.

Substituting,
4 = 1/2(1) + c
therefore, c = 7/2

So the equation of the line passing through (1,4) with slope 1/2 will be:

y = x/2 + 7/2

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