Question

find the value of k if the line joining (k,4) and (-3,12) is perpendicular to the line 3y+4x=20

Answer 1

Ok we know that perpendicular lines have a slope with a negative reciprocal
So if the slope of line A is 1/2 then the slope of the overparticular line B is -2
Do you follow that?

Answer 2

WELCOME TO OPENSTUDY !!!
Have FUN and PLAY RESPONSIBLY !!!
lol

Answer 3

Yah I do

Answer 4

Ok so lets rearrange 3y+4x=20 into slope intercept form ok
Slope intercept form: y=mx+b
Where b is the y-intercept and m is the slope

Answer 5

3y+4x=20

We are trying to isolate the y
Our first step would be to subtract the 4x from both sides
3y+4x-4x=20-4x
3y=20-4x

Answer 6

K

Answer 7

Next step is to get rid of the 3 attached to the y and that is achieved by dividing both sides by 3
\[\frac{3y}{y}=\frac{20}{3}-\frac{4x}{3}\]
\[y=-\frac{4}{3}x+\frac{20}{3}\]
Do you follow what I have done so far?

Answer 8

Yes

Answer 9

Now our equation is in the form y=mx+b

So in that case what is our slope???

Answer 10

-4/3

Answer 11

Yes that is correct

Now the slope of the perpendicular line is the negative reciprocal of the slope of this line ... You familiar with that term?

So basically its the negative reciprocal of -4/3

Answer 12

Ok

Answer 13

Negative reciprocal just means flipping the fraction and changing the sign in front.
So for example if the slope was 3/10

To find the slope of the perpendicular line I would
#1) Flip the fraction so 3/10 ---> 10/3
#2) I would change the sign in front . Now its positive so we will change it to negative
10/3 ---> -10/3

So the slope of the perpendicular line is -10/3

We would follow the same process for the slope -4/3
Can you figure out what the slope of the perpendicular line would be?

Answer 14

3/4

Answer 15

Correct

Answer 16

Ok so we know that the slope of the perpendicular line is 3/4

The equation of the slope is as follows
\[ \text{ Slope }=\frac{ \text{ Change in Y}}{\text{ Change in X}}\]
\[\text{ Slope } = \frac {Y_1-Y_0}{X_1-X_0}\]

Now we were given 2 points above (k,4) and (-3,12)

Let \( (X_0,Y_0)=(k,4)\) so \(X_0=k \) and \( Y_0=4\)

Let \( X_1,Y_1)=(-3,12)\) so \(X_1=-3\) and \(Y-1=12\)

We also know that the slope is 3/4 so using all this information ... plug it into the equation of the slope and solve for k

Answer 17

If you need help just tag me and Ill help you out. But id love if ya attempted it on your own first

Answer 18

@Kainui pls medal me <3

Answer 19

So did you figure it out?

Answer 20

K =2

Answer 21

Were u given options?
I am getting an ugly number

Answer 22

I just wanna confirm I was given the right information
Is it 3y+4x=20?
And are these the 2 points provided (k,4) and (-3,12) ?

Answer 23

Yeah because when you plug it back the equation it works

Answer 24

Plug what back in?

Answer 25

Can you copy and paste the equation? I just wanna dbl check

Answer 26

Never mind but when you have slope intercept and plug in 4 for y and substitute x for k to find k

Answer 27

No its just saying that the line is perpendicular
Meaning that the slope of this line is 3/4

Answer 28

The original was 3y+4x = 20
Slope int. Y= -4/3x +20/3
Using( 4,k)
4=-4/3k + 20/3 to find k because that what they want

Answer 29

\[\text{ Slope } = \frac {Y_1-Y_0}{X_1-X_0}\]
\[\frac{3}{4}=\frac{12-4}{-3-k}\]
Solve for k

Answer 30

Yeah exactly

Answer 31

Umm that aint the way we do it cuz the question never stated that the the point (k,4) was one of the points in the line 3y+4x=20
It was saying that the perpendicular line to 3y+4x=20 has the point (k,4)

Answer 32

So ya when i tried solving for k I got k=41/3
So thats pretty much an ugly number
DO you have any options?

Answer 33

Alright this was the question (find the value of k if the line joining (k,4) and (-3,12) is perpendicular to the line 3y+4x=20) see if that helps but thanks for you help and 2 is correct hope to see you sometime in the future

Answer 34

hmmm Maybe i Misunderstood the whole question lol

Answer 35

All you did was find the point of k when y=4 of the equation 3y+4x=20
So ya plugged in y=4 and solved for k. You didnt into consideration the slope and stuff . All the best :)