Question

Consider the line y=—1/3x—9What is the slope of a line perpendicular tothis line?What is the slope of a line parallel to this line?Slope of a perpendicular line:Slope of a parallel line:

Answer 1

In order to find the slope of a perpendicular line and of a parallel line, first let's identify the slope of the given line, comparing the equation with the slope-intercept model below:

`y=mx+b`

Where m is the slope and b is the y-intercept.

Looking at the given line, we have m = -1/3.

The slope of a perpendicular line has the following relation with the slope of the line:

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

Calculating the slope of the perpendicular line, we have:

`m_2=-(1)/(-(1)/(3))=(1)/((1)/(3))=3`

Therefore the slope of a perpendicular line is m = 3.

The slope of a parallel line is the same as the slope of the given line, so the slope of a parallel line is m = -1/3.