Why is the product of slope of x and y axis is not -1 even if they are perpendicular.

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Solution

Product of slopes of two lines which are perpendicular = -1, is derived from the angles these lines make with x axis.

If we take x axis and y axis alone, this is not applicable as the angle made by y axis with x axis = 90 and tan 90 is not defined. Hence, this identity is cannot be applied in this case. In fact, there is no need to do so, since it is clear that the axes are perpendicular to each other.

It is only in case where lines are differently inclined with x axis, where you need to find the condition for them to be perpendicular to each other.

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Similar questions

Q. Assertion :The lines

x + 3 y = 5, 3 x - y = 9

are perpendicular. Reason: 2 lines are perpendicular if the product of their slopes is -1

True or false?

(a) The equation of the x-axis is x = 0.

(b) The line x = 4 is parallel to y-axis

(d) The lines x = y and x = − y are perpendicular to each other.

(e) The lines x = 9 and y = 9 are perpendicular to each other.

(f) The graph of y = x² is a straight line.

(g) The line y = 3x + 4 does not intersect x-axis.

(h) In a rectangular coordinate system, the coordinate axes are chosen such that they form a pair of perpendicular lines.

Q. What will be the slope if a line is perpendicular to y-axis?

Statement 1 : If two lines are perpendicular, then product of their slopes is –1.
Statement 2: If the product of slopes of two lines is –1, then these lines will be perpendicular.

Q. In the figure above, line

l

intersects the x-axis at

x = - 2

and the y-axis at

y = - 3

. If line m (not shown) passes through the origin and is perpendicular to line

l

, what is the slope of line m ?

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