The lines are perpendicular to each other.
Work Step by Step
RECALL: (1) Parallel lines have the same slope. (2) Perpendicular lines have slopes whose product is $-1$ (negative reciprocals of each other.) (3) The slope-intercept form of a line's equation is $y=mx + b$ where $m$=slope and $(0, b)$ is the line's y-intercept. Write both equations in slope-intercept form to obtain: First Equation: $y+5=-x \\y+5-5=-x-5 \\y=-x-5$ The slope of this line is $-1$. Second Equation: $x-y=2 \\x-y-x=2-x \\-y=2-x \\-y=-x+2 \\-1(-y)=-1(-x+2) \\y=x-2$ The slope of this line is $1$. Since $-1(1)=-1$, the two lines are perpendicular to each other.