SOLUTION: Please help me figure this one out. Find the value of K so that the line through (3,K) and (-1,5) is parallel to the line x + 2y = 4. I substituted zero for y and got x = 4

Algebra ->  Algebra  -> Linear-equations -> SOLUTION: Please help me figure this one out. Find the value of K so that the line through (3,K) and (-1,5) is parallel to the line x + 2y = 4. I substituted zero for y and got x = 4       Log On

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Question 16529: Please help me figure this one out.
Find the value of K so that the line through (3,K) and (-1,5) is parallel to
the line x + 2y = 4.
I substituted zero for y and got x = 4 for x intercept (4,0)
Then substitued 1 or y and got x = 1 for point (1,1)
Where should I go from here. Thanks for any help!
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
First, recall that parallel lines have equal slopes.
Find the slope of the given line by solving the equation for y.
x+%2B+2y+=+4 Subtract x from both sides.
2y+=+-x+%2B+4 Divide both sides by 2.
y+=+%28-1%2F2%29x+%2B+2 Compare with ths slope-intercept form y+=+mx+%2B+b
and you'll see that the slope is -1/2
The formula for the slope of a line is given by: m+=+%28y2+-y1%29%2F%28x2+-+x1%29
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%2F2+=+%285+-+K%29%2F%28-1+-+3%29
-1%2F2+=+%285+-+K%29%2F-4 Multiply both sides by -4
2+=+5+-+K Add K to both sides.
K+%2B+2+=+5 Subtract 2 from both sides.
K+=+3 And there you have it!