Question

an iffy wording, but here i go: this problem "is there a value of K and M such that the two lines are parallel?" also l1(3,9) (-4,7) and l2 (12,M) (K,13) are given. so the preliminary work of finding the slope of line 1 was done, (which is 2/7) b/c 7-9/-4+3 =-2/-7, so u got 2/7. From there it would seem obvious to set up the M and K to equal a 2/7 slope. so i did 13-m/k-12=2/7, and got a value of 11 for M and 19 for K, but you could also use a value of 15 for M and 5 for K which would equal -2/-7 which is still equal to the slope of 2/7. is it possible for two values for M&K? why?

Answer 1

\(\frac{13-m}{k-12} = \frac{2}{7}\)

Answer 2

thats the slope we need for second line ?

Answer 3

yes, but what i am trying to get to the bottom to is if i can use the values that would be 13-m/k-12 = -2/-7, since the slope (2/7) could still be -2/-7 in the equation, thots?

Answer 4

so the values of m and k could either be 11& 19 or 15&5

Answer 5

if we put m = 11, k = 19
if we put m=15, k = 5

?

Answer 6

yes

Answer 7

compute these below ones also :


if we put m=0, we can get k= ?
if we put m=1, we can get k = ?
if we put m=2, we can get k = ?

Answer 8

there would be many possibilities for k & m

Answer 9

there wil be infinity as u can see , for every m value, there wil be a k value, that gives the required slope of 2/7 for the second line

Answer 10

so your concluding so long there is a slope of 2/7 to make the lines parallel, there can be infinite values?

Answer 11

l2 : (12,M) (K,13)

we can choose M, K in many different ways, making the slope of this line l2 to be fixed at 2/7

Answer 12

\(\frac{13-m}{k-12} = \frac{2}{7} \)

here, if u let m=some_value, you would get k=some_other_value

Answer 13

so so many possibile values for M & K

Answer 14

ahh gotcha thanks a bunch, so infinite values?

Answer 15

countless possibilities = infinite

Answer 16

it may make more sense if we visualize it

Answer 17

without solving it all arithmetic way

Answer 18

draw these lines :

1) l1
2) x=12
3) y=13