Question

Are these lines parallel or not:L1 : (2,-1), (5,-7), and L2: (0,0), (-1,2) A. ParallelB.No

Answer 1

So,

Two lines are parallel when their slopes are the same.

So, let's find the slope of each line, and then compare them.

`\begin{gathered} L_1\colon(x_1,y_1)=(2,-1);\text{ }(x_2,y_2)=(5,-7) \\ m=(y_2-y_1)/(x_2-x_1) \end{gathered}`

Replacing the ordered pairs in the equation, we obtain:

`m=(-7-(-1))/(5-2)=(-6)/(3)=-2`

Thus the slope of the first line is -2. Let's use the same process to find the slope of the second line:

`L_2\colon(x_1,y_1)=(0,0);\text{ }(x_2,y_2)=(-1,2)`

Given:

`m=(y_2-y_1)/(x_2-x_1)\to m=(2-0)/(-1-0)=(2)/(-1)=-2`

As you can see, the slope of both lines is the same. So, the lines are parallel.