Question

Find the equation of a line that is perpendicular to the line x=4 and contains the point (-9,-8)

Answer 1

Well, I would first graph those two things

Answer 2

Actually, you take this @mathmale

Answer 3

What is the slope of the line x=4?
What is the slope of any line perpendicular to x=4?

Answer 4

y=-1/4 ?

Answer 5

http://www.freemathhelp.com/combining-like-terms.html

Answer 6

Why y=-1/4? We're discussing slopes only.

Answer 7

oh the slope of the line x=4 would be -1

Answer 8

Could y ou defe nd that statement, please?

Answer 9

yea you subtract x from both sides --> x-x= 4-x --> 0=-x+4

Answer 10

Let's start over, please. What is the slope, if any, of the line x=4?

Answer 11

1

Answer 12

Not quite. What does the graph of the line x=4 look like?

Answer 13

its a straight vertical line from 4 on the x axis

Answer 14

a straight vertical line THROUGH

Answer 15

x=4.

Answer 16

How is the line x=4 related to the y axis?

Answer 17

it isnt they never intersect

Answer 18

Actually, there's a relationship. The line x=4 is _____________________ to the y-axis.

Answer 19

parallel

Answer 20

right.

Next, what is the slope of a vertical line?

Answer 21

y= -1/4

Answer 22

That's a bit far off. How do you figure that a vertical line could have a slope of -1/4?

Have you drawn the line x=4 yet?

Answer 23

Slope = rise over run: rise / run

Answer 24

Note: x=4 tells us that every point on this vertical line is at a distance of 4 units from the y-axis.

Answer 25

yes

Answer 26

Nice graph. Same question: What is the slope of the vertical line x=4?

Answer 27

If the line has a slope, you must be able to illustrate the rise and the run.

Answer 28

ohh i think i got it the slope is -1, but the slope would be -1/8 for a perpendicular line

Answer 29

Unfortunately, those two surmises are not correct. The slope of a vertical line is not -1. nor is the slope of a perpendicular line equal to -1/8.

Answer 30

oh i took the y value and put it as 1/8 because its the negative reciprocal

Answer 31

Look at your own drawing. Look at the vertical line thru x=4, described as x=4.
What is an example of the rise? of the run? what is m = rise/ run?

But, Chick, 4 is not a slope, and therefore you should not be taking the neg. recip. of it.

Answer 32

Looking at the vertical line x=4, what is a sample rise? a sample run?

Answer 33

\[slope=m=\frac{ rise }{ run }\]

Answer 34

ohhh since its a distance of 4 units from the axis its -1/4

Answer 35

a "rise" is a vertical change in positiion.

a "run" is a horiz. change in position.

Looking at the line x=4, do you see that x changes?

Answer 36

no x doesnt change

Answer 37

Concentrate solely on the vertical line x=4. Do you see x changing on that line?

Answer 38

Then the horizontal change, or change in x, is zero.

The vertical change, or change in y, could be any number.

What is the value of 10 / 0?

Answer 39

undefined

Answer 40

Hint: "division by ____________ is undefined."

Answer 41

Division by zero is undefined.
Therefore, the slope of the vertical line x=4 is _________________________ ."

Answer 42

undefined

Answer 43

Correct. And what is the negative reciprocal of that? You know where the line x=4 is. Draw a horiz. line thru it for any y value you want.

Answer 44

ok so i can pick a number and just say y= 1

Answer 45

sure.

Answer 46

draw the line y=1 on your previous graph.

Answer 47

Good. Remembering that the line y=1 is horizontal, and that slope = rise / run,
find the slope of the line y=1.

Answer 48

0

Answer 49

Exactly.

The point-slope form of the eq'n of a str. line is \[y-y _{1}=m(x-x _{1})\]

Please take the given point and subst. its coordinates into this equation of a line with slope m.

In this case our slope, m, has the value _____ .

Answer 50

The given point is (-9,-8).

Answer 51

y+8=0(x+9)
y+8=0
y=-8

Answer 52

Super. Super. That's it.

The line y=-8 is perpendicular to the vertical line x=4 and, additionally, it passes thru the given point (-9,-8).

Answer 53

End of problem.

Answer 54

ok thanks!!

Answer 55

My pleasure.

Review: The equation of the x-axis is _______________
The equation of the y-axis is ___________________

The line y=1 is _____________________ to the x-axis and _________________ to the y-axis.

Answer 56

y=0
x=0

Answer 57

Great. And the 2nd two blanks should read ________________ and __________________ .