Question 16529
First, recall that parallel lines have equal slopes.
Find the slope of the given line by solving the equation for y.

{{{x + 2y = 4}}} Subtract x from both sides.
{{{2y = -x + 4}}} Divide both sides by 2.
{{{y = (-1/2)x + 2}}} Compare with ths slope-intercept form {{{y = mx + b}}}
and you'll see that the slope is -1/2

The formula for the slope of a line is given by: {{{m = (y2 -y1)/(x2 - x1)}}}

Since the new line going through points (3, K) and (-1, 5) is parallel to the given line, the new line will have the same slope as the given line, right?

You can use these facts to find the value of K.

{{{-1/2 = (5 - K)/(-1 - 3)}}}
{{{-1/2 = (5 - K)/-4}}} Multiply both sides by -4
{{{2 = 5 - K}}} Add K to both sides.
{{{K + 2 = 5}}} Subtract 2 from both sides.
{{{K = 3}}} And there you have it!