SOLUTION: Find k so that the line through (4,-1) and (k,2) is a. parallel to 2x + 3y = 6 b. perpendicular to 5x

SOLUTION: Find k so that the line through (4,-1) and (k,2) is a. parallel to 2x + 3y = 6 b. perpendicular to 5x - 2y = -1

Question 146815This question is from textbook
: Find k so that the line through (4,-1) and (k,2) is
a. parallel to 2x + 3y = 6
b. perpendicular to 5x - 2y = -1 This question is from textbook

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find k so that the line through (4,-1) and (k,2) is
a. parallel to 2x + 3y = 6
b. perpendicular to 5x - 2y = -1
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a. Put in form y = mx+b to find the slope m
y = (-2/3)x + 2
m = -2/3
To be parallel, the line has to have the same slope.
m = (y2-y1)/(x2-x1)
-2/3 = (2 - (-1))/(k - 4)
-2/3 = 3/(k-4)
-2(k-4) = 9
-2k+8 = 9
2k=-1
k = -1/2
Check: (2 + 1)/((-1/2) - 4) = 3/(-4.5) = -2/3
------------------
b. The slope m of 5x - 2y = -1 is 5/2.
To be perpendicular, the slope is the negative inverse, -2/5.
m = (y2-y1)/(x2-x1)
-2/5 = (2+1)/(k-4)
Cross multiply
-2(k-4) = 5*3
-2k+8 = 15
2k = -7
k = -7/2
Check (2 + 1)/(-3.5 -4) = 3/(-7.5) = -2/5

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