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:

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

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.

$\text{slope}=\frac{1-2}{5-3}=\frac{-1}{2}=-\frac{1}{2}$

So we have:

$\text{slope parallel line=-}\frac{1}{2}$

And

$\begin{gathered} \text{slope line r}\times slope\text{ line s=-1} \\ -\frac{1}{2}\times slope\text{ line s=-1} \\ \text{slope line s=2} \end{gathered}$

2.

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

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.

$\text{slop}e=\frac{8-(-3)}{-8-(-4)}=\frac{11}{-4}=-\frac{11}{4}$

Then

$\text{slope parallel line=-}\frac{11}{4}$

And

$\begin{gathered} \text{slope line r}\times slope\text{ line s=-1} \\ -\frac{11}{4}\times slope\text{ line s=-1} \\ \text{slope line s=}\frac{4}{11} \end{gathered}$

4.

$\text{slope}=\frac{7-(-9)}{(-2)-3}=\frac{16}{-5}=-\frac{16}{5}$

Then

$\text{parallel line =-}\frac{16}{5}$

And

$\begin{gathered} \text{slope line r}\times slope\text{ line s=-1} \\ -\frac{16}{5}\times slope\text{ line s=-1} \\ \text{slope line s =}\frac{5}{16} \end{gathered}$

5.

$\text{slope}=\frac{-3-(-4)}{1-4}=\frac{1}{-3}=-\frac{1}{3}$

Then

$\text{parallel line=-}\frac{1}{3}$

And

$\begin{gathered} \text{slope line r}\times slope\text{ line s=-1} \\ -\frac{1}{3}\times slope\text{ line s=-1} \\ \text{slope line s=3} \end{gathered}$