Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

If two non-vertical and non-horizontal lines are parallel, then their slopes are equal. If two non-vertical and non-horizontal lines are perpendicular, then the product of their slopes is $-1$. Here, for the first line: $y=4x+5$ The slope, in this form of the equation, is equal to the coefficient of $x$. Hence, the slope of this line is $4$. For the second line: $y=-4x+2$ The sope of this line is $-4$. The slope of the two lines are not equal and their product is not $-1$. Therefore the two lines are neither parallel nor perpendicular.