Question

[4.07]

Choose the slope-intercept equation of the line that passes through the point shown and is perpendicular to the line shown.

Answer 1

y = 1/3x - 8

y = -3x + 12

y = 3x - 24

y = -1/3 - 4

Answer 2

do you know how to find out the gradient of that line?

Answer 3

no i need a walkthrough please

Answer 4

ok you ready?

Answer 5

yup

Answer 6

to find out the gradient of a line, we need to divide the difference in y co-ordinate by the difference in x co-ordinate..

Answer 7

so\[gradient = \frac{ y2-21 }{ x2-x1 }\] where (x1,y1) is one co-ordinate and (x2,y2) is another

Answer 8

so slope

Answer 9

so pick two points on that line...and tell me...

Answer 10

yup

Answer 11

ok one sec

Answer 12

-3/1

Answer 13

huh?

Answer 14

(-3,1) is not on the line

Answer 15

do you mean (1,-3)?

Answer 16

ik thats my answer my two points are (0,-6) and (2,0)

Answer 17

oh.... haha. wait... let me check

Answer 18

so the gradient is 3

Answer 19

-3 or 3

Answer 20

3

Answer 21

OK

Answer 22

how did you get -3/1?

Answer 23

I did y1-y2 not y2-y1

Answer 24

gradient = (0-(-6))/(2-0)
= 6/2
= 3

Answer 25

yeah i understand

Answer 26

now an interesting fact about perpendicular line is that the gradient of perpendicular line multiplied by the gradient of the normal line is -1

Answer 27

since we know the gradient of the normal line, we can calculate the gradient of the perpendicular line..

Answer 28

you with me?

Answer 29

ok so the gradient/slope of the perpendicular line is -1?

Answer 30

no the product of the gradient of the perpendicular line and the normal line is -1

Answer 31

oh ok i get it now

Answer 32

suppose the gradient of the perpendicular line is a and the gradient of the normal line is b, the a x b = -1

Answer 33

yeah ok i understand

Answer 34

since we know the gradient of this normal line is 3 and if we suppose that the gradient of the perpendicular line is 'a'. we can say that
3a=-1
a=-1/3
therefore the gradient of the perpendicular line is -1/3

Answer 35

ok am following you

Answer 36

ok... you see that black point on the graph??

Answer 37

yea

Answer 38

the question want our perpendicular line to go through that point..

Answer 39

(6,-6) the point

Answer 40

the co-ordinate of that point is (6,-6)

Answer 41

yup

Answer 42

do i use y=mx+b here

Answer 43

now we can use the formula \[y-y1=m(x-x1)\] where (x1,y1) i sthe point that the line goes through and 'm' is the gradient of the perpendicular line...

Answer 44

ok

Answer 45

so... subsituting the values gives us...?

Answer 46

so y+6=-1/3(x-6)

Answer 47

yup... but the question wants it is y=mx+b form... so we need to rearrange it...

Answer 48

so -6=-1/3(6)+b

Answer 49

huh....?

Answer 50

hold up hold up

Answer 51

just rearrange
y+6=-1/3(x-6)

Answer 52

ok so y+6=-1/3x-18

Answer 53

nope

Answer 54

y+6=(-1/3)x+2

Answer 55

ok i see what you did

Answer 56

follow me?

Answer 57

-1/3 * 6

Answer 58

ok... now move the 6 from the left side to the right

Answer 59

yup...

Answer 60

y=(-1/3)x+4

Answer 61

small mistake....

Answer 62

-4?

Answer 63

yup....

Answer 64

ok yeah i get confused with that part but you clarified it

Answer 65

y+6-6=(-1/3)x+2-6
y=(-1/3)x-4...

Answer 66

so now just by rearranging the equation you ended up with y=mx+b form...

Answer 67

can you see that? m=(-1/3) and b =-4

Answer 68

ok

Answer 69

and that is it...

Answer 70

thanks homie

Answer 71

no problem...

Answer 72

good luck with these kind of questions..