How do you find the value of k if the line through the points (2k-2,27-k) and (5k-5,3k+4) is parallel to the line through the point (15,7) and (-9,-6)?

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Answer 1 · 2018-06-20T13:37:16

If they are parallel then the gradients are the same

#[3k+4-(27-k)]/[5k-5-(2k-2)]=[7- -6]/[15- -9]#

Remove the brackets

#[3k+4-27+k]/[5k-5-2k+2]=[7+6]/[15+9]#

Collect like terms

#[4k-23]/[3k-3]=[13]/[24]#

Multiply #(4k-23)# by 24
Multiply 13 by #(3k-3)#

#96k-552=39k-39#

Subtract #39k#

#57k-552=-39#

Add 552

#57k=513

Divide by 57

#k=9#