Question

For each line identified by two points, state the slope of a line parallel and the slope ofa line perpendicular to it.1.A(3, 2) and B(5, 1)2. C(-2,0)and D（-2,一4)3. M(-4, -3) and N(-8, 8)4. X(3, -9)and Y(-2,7)5. R(4, -4) and S(1, -3 )

Answer 1

A line parallel to each given line will have equal slopes. Lines perpendicular to each other have the product of their slopes equal to -1. We can summarize like this:

`\begin{gathered} \text{parallel lines}\rightarrow equal\text{ slopes} \\ \text{perpendicular lines}\rightarrow slope\text{ line r}* slope\text{ line s=-1} \end{gathered}`

Let's do the math and get each slope.

The slope of a line can be calculated using the formula:

`\text{slope}=\frac{difference\text{ of y's coordinates}}{\text{difference of x's coordinates}}`

1.

`\text{slope}=(1-2)/(5-3)=(-1)/(2)=-(1)/(2)`

So we have:

`\text{slope parallel line=-}(1)/(2)`

And

`\begin{gathered} \text{slope line r}* slope\text{ line s=-1} \\ -(1)/(2)* slope\text{ line s=-1} \\ \text{slope line s=2} \end{gathered}`

2.

`\text{slope}=(-4-0)/(-2-(-2))=(-4)/(0)\rightarrow slope\text{ can't be calculated}`

On this case, we have a perpendicular line to the x-axis.

A parallel line to this can be any vertical line which equation is:

`\begin{gathered} \text{parallel line }\rightarrow x=k,\text{ where k is a constant} \\ \text{slope}=there\text{ isn't} \end{gathered}`

A perpendicular line to this can be any horizontal line which equation is:

`\begin{gathered} \text{perpendicular line}\rightarrow y=k\text{ where k is a constant} \\ \text{horizontal line}\rightarrow slope=0 \end{gathered}`

3.

`\text{slop}e=(8-(-3))/(-8-(-4))=(11)/(-4)=-(11)/(4)`

Then

`\text{slope parallel line=-}(11)/(4)`

And

`\begin{gathered} \text{slope line r}* slope\text{ line s=-1} \\ -(11)/(4)* slope\text{ line s=-1} \\ \text{slope line s=}(4)/(11) \end{gathered}`

4.

`\text{slope}=(7-(-9))/((-2)-3)=(16)/(-5)=-(16)/(5)`

Then

`\text{parallel line =-}(16)/(5)`

And

`\begin{gathered} \text{slope line r}* slope\text{ line s=-1} \\ -(16)/(5)* slope\text{ line s=-1} \\ \text{slope line s =}(5)/(16) \end{gathered}`

5.

`\text{slope}=(-3-(-4))/(1-4)=(1)/(-3)=-(1)/(3)`

Then

`\text{parallel line=-}(1)/(3)`

And

`\begin{gathered} \text{slope line r}* slope\text{ line s=-1} \\ -(1)/(3)* slope\text{ line s=-1} \\ \text{slope line s=3} \end{gathered}`