Question

Find equations of the lines passing through (1, 3) and having the following characteristics.
(a) Slope of -2/3
(b) Perpendicular to the line x + y = 0
(c) Passing through the point (2, 4)
(d) Parallel to the x-axis

Answer 1

@ParthKohli

Answer 2

@waterineyes

Answer 3

see when slope and one point is given:

Use:

\[y-y_1 = m(x - x_1)\]

Can you plug in the values??

m = -2/3 and (x1, y1) = (1, 3)

Can you do it??

Answer 4

Hmm... but i don't understand the ab,c,d .. do I just get one final answer, or four?

Answer 5

@waterineyes

Answer 6

You have four different answers..

I am solving for a part..

Answer 7

are you solving for part a?

Answer 8

Yes i am..

Answer 9

See I have provided you the formula can you plug in the value and solve??

Answer 10

sure, let me try

Answer 11

Take your time..

Answer 12

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

Answer 13

Yes..
Do you want to solve it further or not??

Or are their choices provided for this question??

Answer 14

there aren't choices

Answer 15

@waterineyes

Answer 16

So i don't think it matters. can u help with b,c, and d? :)

Answer 17

If its perp, the slope should be 3/2

Answer 18

See, equation of perpendicular line is given..

No, our first question is over..

You are using the slope of first part...

Answer 19

We have a.. but we need b, c, and d.

Answer 20

Oh right, never mind

Answer 21

Wait dear let me explain I will make you clear each and everything..

Answer 22

x+y=0

Answer 23

Yes now can you find slope from this equation x = y = 0??

Answer 24

*+

Answer 25

Is it -1

Answer 26

Yes you are right..
Now can you tell me the slope of the line that is perpendicular to it??

Answer 27

1

Answer 28

Yes..

Now m= 1 and (x1, y1) = (1,3) [given]

Can you find its equation??
Same procedure..

Answer 29

y-y1=1(x-x1)

Answer 30

y-3=1(x-1)

Answer 31

Yes now you are right that is B part..

Answer 32

ok cool. now c

Answer 33

passing thru 3,4

Answer 34

y-4= m(x-3) now what slope goes in m?

Answer 35

When two points are given we use Two point formula:

\[\large \frac{y - y_1}{y_2 - y_1} = \frac{x-x_1}{x_2 - x_1}\]

Answer 36

What values would go in that..

Answer 37

(x1, y1) = (1,3) and (x2, y2) = (2, 4)

Answer 38

I meant 2, not 3 !!

Answer 39

Ok let me plug

Answer 40

y-3/4-3=x-1/2-1 ??

Answer 41

Ok take your time..

After plugging in use cross multiplication to solve further..

Answer 42

y-3/1 = x-1/1 is that right so far.

Answer 43

Yes you are going right..

Answer 44

y-3=x-1

Answer 45

y - 3 = x - 1

That is answer for C part..

Answer 46

yay! okay lastly d

Answer 47

parallel to x-axis

Answer 48

D) see always remember the line parallel to x axis will have equation as : \(y = \pm c\)

and line parallel to y axis has equation \(x = \pm c\)

Here the required equation is:

\(y = \pm c\)

Getting??

Answer 49

Yes

Answer 50

And one thing you must remember that:

Slope of Line parallel to X-axis will be 0

and Slope of Line perpendicular to X-axis or Parallel to Y-axis will be Infinity..

So, here m = 0

Answer 51

ok so we have y=+/-c, with the slope as 0...