Question

Help!
The equation of line WX is y = −2x − 5. Write an equation of a line perpendicular to line WX in slope-intercept form that contains point (−1, −2).

Answers:

y = 1 over 2x + 3 over 2

y = negative 1 over 2x + 3 over 2

y = 1 over 2x − 3 over 2

y = − 1 over 2x − 3 over 2

Answer 1

lol guess what step 1 is?

Answer 2

find the slope?

Answer 3

right, find the slope of \( y = −2x − 5\) with your eyes

Answer 4

?

Answer 5

whoops -2

Answer 6

k good

Answer 7

step 2 is to know that the perpendicular line will have slope that is the "negative reciprocal" i.e. \(\frac{1}{2}\)

Answer 8

the slope is going to be negative reciprocal of the given slope which is 1/2

Answer 9

im confused

Answer 10

lets back up then

Answer 11

you got the slope of \( y = −2x − 5\) is \(-2\) right?

Answer 12

yes

Answer 13

questions asks for
equation of a line PERPENDICULAR

Answer 14

that means the slope will be the "negative reciprocal" which is a fancy way of saying "flip it and change the sign"

Answer 15

i.e for \(-2\) the "negative reciprocal" is \(\frac{1}{2}\)

Answer 16

so change it to positive

Answer 17

clear now or no?

Answer 18

exactly
flip it and change the sign

Answer 19

so 1/2

Answer 20

if it is negative, make it positive
if it is positive, make it negative
right

Answer 21

yes

Answer 22

we good now?

Answer 23

yes

Answer 24

substitute the slope 1/2 and the given point (-1,-2) in y-y1=m(x-x1) and solve p.s.m=slope=1/2

Answer 25

step 3
point is \((−1, −2)\) be careful with the signs
point slope formula gives
\[y+2=\frac{1}{2}(x+1)\]

Answer 26

now some fraction arithmetic

Answer 27

so y=1/2x+2

Answer 28

yes

Answer 29

not quite

Answer 30

pretty close

Answer 31

wait what?

Answer 32

\[y+2=\frac{1}{2}(x+1)\]
\[y+2=\frac{1}{2}x+\frac{1}{2}\]

Answer 33

now subtract \(2\) from both sides

Answer 34

ok i am waiting
is it clear how to remove the parentheses?

Answer 35

k holding

Answer 36

y=1/2x - 3/2 is the answer

Answer 37

y=1/2x-3/2

Answer 38

yup

Answer 39

thanks! can you help me with 2 more?

Answer 40

you got that negative reciprocal thing now?

Answer 41

sure

Answer 42

yes you change it to positive but hold on let me get the question

Answer 43

k i'll wait

Answer 44

Line QR contains (2, 8) and (3, 10) Line ST contains points (0, 6) and (−2, 2). Lines QR and ST are

Answers:
parallel, because the product of the slopes is −1

perpendicular, because the product of the slopes is −1

parallel, because the slopes are the same

perpendicular, because the slopes are the same

Answer 45

we need to find the slope of both

Answer 46

find the slopes of both the lines and then compare the formula for finding the slope=(y2-y1)/(x2-x1)

Answer 47

slope of \( (2, 8),(3, 10) \) \[m=\frac{10-8}{3-2}=\frac{2}{1}=2\]

Answer 48

\[(0, 6), (−2, 2)\] let me know what you get

Answer 49

alright give me a sec

Answer 50

k

Answer 51

2

Answer 52

therefore the answer is C.

Answer 53

k good

Answer 54

so the slopes are the same, they are both \(2\)

Answer 55

so it is c

Answer 56

that means they are parallel

Answer 57

yeah, it is always C anyway

Answer 58

ok last one

Answer 59

k

Answer 60

The equation of line CD is (y−3) = − 2 (x − 4). What is the slope of a line perpendicular to line CD?

Answers:
1 over 2

2

negative 1 over 2

−2

Answer 61

slope is ?

Answer 62

i mean what is the slope of \( (y−3) = − 2 (x − 4)\) ?

Answer 63

since it's in point slope dont we need to put it in slope intercept

Answer 64

oh ya hold on let me solve it

Answer 65

no you don't need to change the form
it is in the point - slope form, all you need is the slope

Answer 66

slope intercept form

Answer 67

you see it with your eyes already

Answer 68

-3?

Answer 69

oh no

Answer 70

im confused now

Answer 71

\[(y−3) = \color{red}{− 2} (x − 4)\]

Answer 72

its -2 right

Answer 73

right

Answer 74

now recall that "negative reciprocal" thing

Answer 75

so postive 2

Answer 76

flip it

Answer 77

1/2

Answer 78

"negative reciprocal" has two words, they don't waste words in math
yeah \(\frac{1}{2}\)

Answer 79

so the final answer is 1/2

Answer 80

yes it is

Answer 81

lol 'final answer'

Answer 82

ok i understand now, thank you!

Answer 83

who wants to pass a math class?

Answer 84

yw, hope it is more or less clear