Parelle to Perpendicular

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Tiger-T

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

A) 4/3; 10/3
B)16/3; 10/3
C) 4/3: 2/3
D) 16/3; 2/3

subject: 3y = -2 + 5x
Y = -2/3 + 5/3x
-2 – k/ 1-3 = -2-k/-2
Cross multiply
4 – 2k = 2
4 + 2 = 6
K = 1

Perpendicular

3x + 2y = 6
2y = 6 – 3x
Y = 6/2 – 3/2
2-2/3-6 = -3

Perpendicular to 4y+5x=1
Making y the subject
4y = 1 – 5x
Y = ¼ - 5/4x
= -5/4 perpendicular = 4/5
So 4/5 = 1 or -4/4
Cross multiply
16 – 4k = -20
16 + 20 = 4k
K = 9

I have found this solution to this type of problem, but it does not tell wether it is A,B,C, or D.
 
Tiger-T said:
Find k so that the line through (3, k) and (1, -2) is parallel to 5x - 3y = -2 Find k so that the line is perpendicular to 3x + 2y = 6.

A) 4/3; 10/3
B)16/3; 10/3
C) 4/3: 2/3
D) 16/3; 2/3

subject: 3y = -2 + 5x <<< This is incorrect. It should be:

3y = 5x + 2

Y = -2/3 + 5/3x
-2 – k/ 1-3 = -2-k/-2 <<< What are you doing here?

slope of line through given points = (-2-k)/(1-3) = (2+k)/2

for this to be parallel with 5x - 3y = -2, we have

(2+k)/2 = 5/3

6 + 3k = 10

k = 4/3

Cross multiply
4 – 2k = 2
4 + 2 = 6
K = 1

Perpendicular

3x + 2y = 6
2y = 6 – 3x
Y = 6/2 – 3/2
2-2/3-6 = -3

Perpendicular to 4y+5x=1
Making y the subject
4y = 1 – 5x
Y = ¼ - 5/4x
= -5/4 perpendicular = 4/5
So 4/5 = 1 or -4/4
Cross multiply
16 – 4k = -20
16 + 20 = 4k
K = 9

I have found this solution to this type of problem, but it does not tell wether it is A,B,C, or D.
Click to expand...

Please redo the problem - paying attention to the arithmatic.
 
Thank you Khan, this narrowed it down to A or C. I have a 50/50 chance now. I appreciate you helping find my mistakes!


Subhotosh Khan said:
[quote="Tiger-T":2t7vthrb]Find k so that the line through (3, k) and (1, -2) is parallel to 5x - 3y = -2 Find k so that the line is perpendicular to 3x + 2y = 6.

A) 4/3; 10/3
B)16/3; 10/3
C) 4/3: 2/3
D) 16/3; 2/3

subject: 3y = -2 + 5x <<< This is incorrect. It should be:

3y = 5x + 2

Y = -2/3 + 5/3x
-2 – k/ 1-3 = -2-k/-2 <<< What are you doing here?

slope of line through given points = (-2-k)/(1-3) = (2+k)/2

for this to be parallel with 5x - 3y = -2, we have

(2+k)/2 = 5/3

6 + 3k = 10

k = 4/3

Cross multiply
4 – 2k = 2
4 + 2 = 6
K = 1

Perpendicular

3x + 2y = 6
2y = 6 – 3x
Y = 6/2 – 3/2
2-2/3-6 = -3

Perpendicular to 4y+5x=1
Making y the subject
4y = 1 – 5x
Y = ¼ - 5/4x
= -5/4 perpendicular = 4/5
So 4/5 = 1 or -4/4
Cross multiply
16 – 4k = -20
16 + 20 = 4k
K = 9

I have found this solution to this type of problem, but it does not tell wether it is A,B,C, or D.
Click to expand...

Please redo the problem - paying attention to the arithmatic.[/quote:2t7vthrb]
 
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