Determine whether the graphs of the given equations are parallel, perpendicular, or neither.
y=5x+9
y=-5x+4
To determine if the graphs of the given equations are parallel, perpendicular, or neither, we compare their slopes.
The given equations are in slope-intercept form, y = mx + b, where m is the slope.
Equation 1: y = 5x + 9
The slope of equation 1 is 5.
Equation 2: y = -5x + 4
The slope of equation 2 is -5.
Two lines are parallel if their slopes are equal, so since the slope of equation 1 (5) is not equal to the slope of equation 2 (-5), the graphs of the equations are not parallel.
Two lines are perpendicular if the product of their slopes is -1. The product of the slope of equation 1 (5) and the slope of equation 2 (-5) is -25, which is not equal to -1. Therefore, the graphs of the equations are not perpendicular either.
In conclusion, the graphs of y = 5x + 9 and y = -5x + 4 are neither parallel nor perpendicular.