Question

9. Determine whether the statement is always, sometimes, or never true. Two lines with positive slopes are parallel A) Always B) Sometimes C) Never 10. Determine whether the statement is always, sometimes, or never true. Two lines with the same slope and different y-intercepts are perpendicular. A) Always B) Sometimes C) Never

Answer 1

Answer:

A) Sometimes true

B) Never true

Step-by-step explanation:

We have to determine whether the given statement is always, sometimes, or never true.

A)  Two lines with positive slopes are parallel  

The given statement is sometimes true. It cannot be always true. The lines with same slope are parallel. Thus, two lines with same positive slope will be parallel but nothing could be said about lines with unequal positive slopes.

B) Two lines with the same slope and different y-intercepts are perpendicular.

The given statement is never true as for two lines to be perpendicular the product of their slopes should be -1.

Answer 2

Answer:- $\text{Two lines with positive slopes are parallel}\rightarrow\text{B) Sometimes}\\\text{Two lines with the same slope and different y-intercepts are perpendicular.}\rightarrow\text{C) Never}$

Explanation:-

We know that, two lines with same slope are parallel.

Thus two lines with same positive slopes are parallel.

⇒Two lines with positive slopes are sometimes parallel.

Two lines with same slope can never be perpendicular to each other as they must be parallel.