Determine whether the graphs of the given equations are parallel, perpendicular, or neither.
y = x + 9
y = -x + 4
To determine if two lines are parallel or perpendicular, we need to compare their slopes.
The given equations are in slope-intercept form (y = mx + b), where m is the slope of the line.
For the equation y = x + 9:
The slope of this line is 1.
For the equation y = -x + 4:
The slope of this line is -1.
Since the slopes of the two lines are negative reciprocals of each other (-1 * 1 = -1), the graphs of the equations are perpendicular.