Question

Are the following two slopes going to make lines that are parallel, perpendicular, or neither?m=-4/1m=1/4

Answer 1

We are given the slopes of two lines.

`m_1=-(4)/(1)\quad \text{and}\quad m_2=(1)/(4)`

Recall that two lines are said to be parallel if they have equal slopes.

Since the given slopes are not equal then we know that they are not parallel.

Recall that two lines are said to perpendicular if their slopes are negative reciprocal of each other.

`m_1=-(1)/(m_2)`

For the given case, we see that the given slopes are indeed negative reciprocal of each other.

Therefore, the two lines with the given slopes are perpendicular.