Finding gradient of perpendicular lines

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What will be the gradient of a vertical line and a horizontal line? Both are perpendicular to each other, and I know the product of their gradients must be $-1$, but that is for slanted lines. What if the lines are parallel to the axes? Horizontal lines have zero gradient and vertical have infinity, so what will be there product? Also, can you tell why perpendicular lines have to have $-1$ gradient?