The given equations are:
1) y = 4x + 1
2) y = -4x - 2
To determine whether the graphs of these equations are perpendicular or parallel, we can examine the slopes of the lines represented by the equations. The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line.
In the first equation (y = 4x + 1), the slope is 4.
In the second equation (y = -4x - 2), the slope is -4.
When two lines are perpendicular, the product of their slopes is -1. If the product is not -1, then the lines are not perpendicular.
Let's calculate the product of the slopes:
4 * (-4) = -16
Because the product of the slopes is not -1, the lines represented by the given equations are not perpendicular to each other.
To determine if they are parallel, we can compare the slopes directly. Since the slopes are 4 and -4, which are negative reciprocals of each other, the lines are in fact perpendicular. I apologize for the confusion in my initial response.