You need to remember that the the slope of a line denotes the value of tangent of angle made by the line to x axis.
You should come up with the notation: `m_x = tanalpha ` (the tangent of angle made by x axis to itself), `m_y = tan beta ` (the tangent of angle made by y axis to x axis).
Since x and y axis are orthogonal, hence the angle between the two axis need to be `pi/2` .
`beta - alpha = pi/2 =gt tan (beta - alpha) = tan (pi/2) = +-oo`
You need to expand the formula `tan (beta - alpha) = (tan beta - tan alpha)/(1 + tan beta*tan alpha)` .
Since `tan (beta - alpha) = +-oo =gt (1 + tan beta*tan alpha) = 0 =gt tan beta*tan alpha = -1`
Plugging `tan alpha = m_x ` and `tan beta = m_y` yields: `m_x*m_y` = -1.
Hence , the product of slopes of x and y axis is `m_x*m_y` = -1.