SOLUTION: find k so that the line thru (4,-1) and (k,2)is a). parallel to 2x+3y=6 b). perpendicular to 5x-2y= -1 pls show work so that i can see where i went wrong thank in advance

Question 97444: find k so that the line thru (4,-1) and (k,2)is
a). parallel to 2x+3y=6
b). perpendicular to 5x-2y= -1
pls show work so that i can see where i went wrong
thank in advance

Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
find k so that the line thru (4,-1) and (k,2)is
a). parallel to 2x+3y=6
b). perpendicular to 5x-2y= -1
a) slope intercept form: y=mx+b m=slope
2x+3y=6
subtract 2x from both sides. 3y=-2x+6
divide 3 into both sides. y=-(2/3)x+2
m=-2/3 this is also the slope of (4,-1) and (k,2)
point slope form: y-y[1]=m(x-x[1])
-1-2=-2/3(4-k)
-3=-8/3-(-2/3k)
-3=-8/3+2/3k
add 8/3 to both sides. -1/3=2/3k
multiply 3/2 times both sides. k=-1/2=-.5 Ans.
.
b) 5x-2y= -1
subtract 5x from both sides. -2y=-5x-1
divide -2 into both sides. y=2.5x+.5
m=5/2
for perpendicular line m=-1/m[1]=-2/5=-.4
point slope form: y-y[1]=m(x-x[1]) for(4,-1) and (k,2)
-1-2=-.4(4-k)
-3=-1.6+.4k
add 1.6 to both sides: .4k=1.4
divide.4 into both sides. k=3.5 Ans.
Ed

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