Question

State whether the graphs of the following equations are parallel, perpendicular, or neither.x + y = 5 x – y = 5

Answer 1

Transform the two equations into their slope-intercept form, as shown below

$\begin{gathered} x+y=5 \\ \Rightarrow y=-x+5 \\ \text{and} \\ x-y=5 \\ \Rightarrow y=x-5 \end{gathered}$

We say that two lines are parallel if they have the same slope; on the other hand, two lines are perpendicular if the product of their slopes is equal to -1.

The slope of x+y=5 is -1, and the slope of x-y=5 is 1; then,

$-1\cdot1=-1$

Thus, the two lines are perpendicular.