Determine whether the graphs of the given equations are​ parallel, perpendicular, or neither.

Question

y = x + 9
y = -x + 4

Answer 1

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.