Question

A line has a slope of 3. What is the slope of a line parallel to this? A line has a slope of -1/2. What is the slope of a line perpendicular to this?

Answer 1

a) The slope of a line parallel to this is 3

b) the slope of a line perpendicular to this is 2

Step-by-step explanation:

a) The slope of a line = 3

For the second line to be parallel to the first line, the slope will be the same.

As a result, the slope of the second line = 3

Using an example:

From the diagram, we see both have a slope of 3 and are parallel

The slope of a line parallel to a line with slope 3 is 3

B) The slope of a line = -1/2

For a line to be perpendicular to another line, the slope of the one line will be the negative reciprocal of the slope of the other line

since we slope of one line as -1/2

`\begin{gathered} \text{reciprocal of second line = }(1)/(-(1)/(2))\text{ = 1 }/\text{ -}(1)/(2) \\ \text{reciprocal of second line = 1 }*\text{ }(2)/(-1)\text{ = 2/-1} \\ \text{reciprocal of second line = -2} \end{gathered}`

negative reciprocal of the slope = negate the result of the reciprocal

negative reciprocal of the slope = -(-2)

negative reciprocal of the slope = 2

Using an example:

From the graph, we see the slope -1/2 and slope 2 give perpendicular lines

The slope of a line perpendicular to a slope of -1/2 is 2