Question

Your friend claims that if a line has a slope less than 1, then any line perpendicular to it must have a positive slope. Is your friend correct?. Explain your reasoning

Answer 1

Answer:

The friend's claim is not correct

Step-by-step explanation:

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal yo -1)

Example

A given line has a slope of $m_1=1/2$  ---> (is less than 1)

the slope of the line perpendicular to the given line is equal to

$m_1*m_2=-1$

substitute

$(1/2)*m_2=-1$

$m_2=-2$

so

the perpendicular line don't have a positive slope

therefore

The friend's claim is not correct