Question

select whether the pair of lines is parallel, perpendicular, or neither.

Explanation:

Step1: Find the slope of line \(JK\)

Let \(J(-1, 3)\) and \(K(-1,-2)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For line \(JK\), \(x_1=-1,y_1 = 3,x_2=-1,y_2=-2\). Then \(m_{JK}=\frac{-2 - 3}{-1-(-1)}=\frac{-5}{0}\), which is undefined (vertical - like behavior in this case, but we can also use the concept of rise - over - run from grid points. The line \(JK\) moves down 5 units (from \(y = 3\) to \(y=-2\)) while \(x\) remains the same (\(\Delta x=0\)).

Step2: Find the slope of line \(LM\)

Let \(L(1,2)\) and \(M(1,-2)\). Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), with \(x_1 = 1,y_1=2,x_2=1,y_2=-2\). Then \(m_{LM}=\frac{-2 - 2}{1 - 1}=\frac{-4}{0}\), which is undefined (vertical - like behavior in this case, but we can also use the concept of rise - over - run from grid points. The line \(LM\) moves down 4 units (from \(y = 2\) to \(y=-2\)) while \(x\) remains the same (\(\Delta x=0\)).

Step3: Determine the relationship between the lines

Two lines are parallel if they have the same slope. Since both lines \(JK\) and \(LM\) have an undefined slope (they are both vertical lines, as we can observe from the fact that for any two points on each line, the \(x\) - coordinate is constant).

Answer:

parallel