Determine the value of k that will make each pair of lines parallel

[kiel]

I'm lost in this number, I solved value of k that will make it perpendicular which is m¹ • m² but for this question "that will make it parallel" im not sure if ill us m¹m² or wtvr. I just need help on what to do/which solution. thanks youu!.

 

[kiel]

i am having trouble on how to do this, I solved value of k that will make perpendicular which is m¹ • m² but for this value of k that will make each pair parallel idk what solution to use if ill use m¹m² or wtvr. I just really need help on what to do/solution. Thank you!

 

[Deleted member 4993]

View attachment 24283 i am having trouble on how to do this, I solved value of k that will make perpendicular which is m¹ • m² but for this value of k that will make each pair parallel idk what solution to use if ill use m¹m² or wtvr. I just really need help on what to do/solution. Thank you!

What are the slopes of the lines in question?

What is the relationship between:

the slopes of the parallel lines?​

View attachment 24283

 

[HallsofIvy]

Did you notice that, in the first problem, the coefficient of x in the first equation is 4 and in the second equation it is 8. That coefficient has been multiplied by 2! The coefficient of y in the first equation is -3. In order to be parallel (have the same slope as Subhotosh Kahn suggested) that must be multiplied by 2 also.

In the second problem, the coefficient of x in the first equation is 2 and in the second equation it is 4. What has it been multiplied by? The coefficient of y in the first equation is -7. What must it be multiplied by to make the lines parallel?

 

[Steven G]

Stop trying to do math by formulas. If two lines are parallel then they must have the same slope. So I will find the slope of both lines, set them equal to one another and solve for k.

What is written above is logical thinking. There was no formulas mentioned at all. True, in order to find the slopes you may need to use a formula but to think through how to do this problem did not involve any formulas.

 

[Steven G]

Note that Ax+By = C and Ax + By = D are parallel. As Dr Halls suggested just get the coefficients of x and y to be the same. This works because Ax+By =C and kAx + kBy = kC are the same lines (as long as k is not 0)