Question

If two lines are parallel which statement must be true? A.Their slopes are zero. B.Their slopes are negative reciprocals. C. Their slopes are undefined. D.Their slopes are equal

Answer 1

D. Their slopes are equal

Explanation:

Answer 2

D

Explanation:

Parallel lines have the same gradient.

A line with a slope of zero is a horizontal line. Although two lines that have a slope of zero will result in two parallel lines, not all parallel lines are horizontal lines. Since the question is asking for which statement must be true, option A is incorrect.

If the slopes of two lines are negative reciprocals, they are perpendicular to each other. This is because the product of the gradients of 2 perpendicular lines is -1. Let the gradient of the first line be A and the other be B.

AB= -1

`A = - ( 1)/(B)`

`B = - (1)/(A)`

Thus, option B is incorrect too.

Undefined slopes gives vertical lines. Like option A, if two lines have an undefined slope, they will be parallel to each other. However since parallel lines are nit necessarily vertical lines, option C is also incorrect.