The X axis has slope 0 and the Y axis is having a slope infinity.Then how do you justify that 0xinf. is not = -1 ?

Expert Answers
sciencesolve eNotes educator| Certified Educator

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.