Question

if each of the following represents the slope of a line,(or line segment,) give the slope a line that is perpendicular to it

Answer 1

We know that the product of to slope of perpendicular lines is always equal to 1, so for a) we have that

`\begin{gathered} (4)/(3)\cdot m^(\prime)\text{ = -1} \\ m^(\prime)\text{ = (-1)}(3)/(4) \\ m^(\prime)\text{ = }(-3)/(4) \end{gathered}`

The answer is: the slope of the line perperdincular is m' = -3/4.

Now for b) we have that

`\begin{gathered} -(3)/(7)\cdot\text{ m' = -1} \\ m^(\prime)\text{ = (-1)}\cdot(-(7)/(3)) \\ m^(\prime)\text{ = }(7)/(3) \end{gathered}`

The answer is: the slope of the line perperdincular is m' = 7/3.

Now for c) we have that

`\begin{gathered} 4\cdot m^(\prime)\text{ = -1} \\ m^(\prime)\text{ = }(-1)/(4) \end{gathered}`

The answer is: the slope of the line perperdincular is m' = -1/4.

Now for d) we have that

`\begin{gathered} -(1)/(3)\cdot m^(\prime)\text{ = -1} \\ m^(\prime)\text{ = (-1)}(-3)/(1)\text{ } \\ m^(\prime)\text{ = 3} \end{gathered}`

The answer is: the slope of the line perperdincular is m' = 3.

Now for e) we have that

`\begin{gathered} 1\cdot\text{ m' = -1} \\ m^(\prime)\text{ = }(-1)/(1) \\ m^(\prime)\text{ = -1} \end{gathered}`

The answer is: the slope of the line perperdincular is m' = -1.