Question

Indicate the equation of the given line in standard form.

The line with slope 9/7 and containing the midpoint of the segment whose end points are (2, -3) and (-6, 5).

Answer 1

go @apoorvk pwn it ;)

Answer 2

we're all watching you...

Answer 3

lol

Answer 4

Wow. Great. let's do this then. -_-

O shell from the sea, with or without an oyster inside...


Do you know how to find the mid-point of a segment whose two end points are given?

Answer 5

nope... ._. vacation stole my brain

Answer 6

Oh no problem, buy a new one from Walmart then. (come cheap these days)

Answer 7

Lol jokes apart,

Answer 8

ehh okay

Answer 9

The midpoint 'M' of segment between two points (x1,y1) and (x2,y2) is:
\[M = (\frac{x_1 + x_2}2 , \frac{y_1 + y_2}2)\]

Does this^ bring back some distant faded memories of a certain "mid-point formula"?
Can you use this?

Answer 10

no it does not bring memories

Answer 11

Well, forget the non-existent memories then, can you just this formula to find out the mid-point of the two points (2,-3) and (-6,5) ?


You just have to substitute the values.

Answer 12

kay

Answer 13

Hmm, so what would the midpoint be?

Answer 14

2,-3

Answer 15

*facepalm*

(2,-3) is one of those points, how can it be the mid-point as well??

Answer 16

-2,1

Answer 17

.-.

Answer 18

Ahaa... right now! Good good. Now the next part.

The equation of a line in its slope-intercept form is:

\[y = mx +c\]

Here, m = slope, and c = constant.


For, now you know the slope of the line required is 9/7.

So, this lines equation in terms of the unknown 'c' would be:

\[y = \frac 9 7 x + c\]


Okay with this^?

Answer 19

wait... there cant be no fractions

Answer 20

Yeah, no probs, we will rearrange the whole thing later on.. Just do as I say for now.

Answer 21

ok

Answer 22

so, we need to find out 'c' now right?

Answer 23

right

Answer 24

Okay so we know, that this line passes through that mid-point (-2,1) that we found out earlier. So, (-2,1) must satisfy the equation of the line.

so let's substitute x=-2 and y=1 in the equation of the line we have so far, and find out 'c'.

can you do this? i think you can...

Answer 25

i cant..

Answer 26

1 = 9/7 (-2) + c

Answer 27

yeah, just like @jollysailorbold says^

I just put in x = -2, and y = 1 in the equation, and I get:
\[1 = \frac 9 7 (-2) + c\]


now, can you solve this and find out the value of 'c'?

Answer 28

12?

Answer 29

\[ c = 1 + 2 \times\frac 9 7\]\[or, c = 1 + \frac {18} 7\]

so, what's 'c' then?

Answer 30

1 18/7 ??

Answer 31

\[c = 1 + \frac {18} 7 = \frac{7 + 18}{7} = ??\]

Answer 32

:/ i dont get itt

Answer 33

can you add two fractions? Do you know how this is done?

Answer 34

yes..

Answer 35

So what's the trouble here?
You just need to add 1 and 18/7 !
Let's go slow-motion then.
\[c = 1 + \frac {18} 7\]\[ =\frac1 1 + \frac {18} 7\]\[ = \frac {7\times 1} {7 \times 1} + \frac {18} 7\]\[ = \frac 7 7 + \frac {18} 7\]\[= \frac{7 + 18}{7} = ??\]

Answer 36

25/7

Answer 37

Finally. -_-

yeah, so we found out what Mr. 'c' is.
so, in the equation of the line we had had in terms of x and y, that is, this one:
\[y = \frac 9 7 x + c\]

I just replace 'c' with it's obtained value.

What equation do I have?

Answer 38

hahahaha omg you just made me laugh

Answer 39

Do I have
\[y = \frac 9 7 x + \frac {25} 7\]

??

Answer 40

yeah

Answer 41

the answers can be in fraction form

Answer 42

You will make me cry soon though. -_-

jus' kidding. xD

Okay, so we are almooooost there.

What I have is the equation of the line in slope intercept form. But we can't have the fractions.
So what do I do? there's a '7' in the denominator. Ohkay, ohkay, Mr. '7', you're goin' up. -.-

I multiply both sides by 7. What do I get then?

Answer 43

can be or "can't" be?

Answer 44

wait....waht doi do?

Answer 45

omg this is like... only one question!!!! and like.... its been 1 hr!!!!!

Answer 46

I have:
\[y = \frac 9 7 x + \frac {25} 7\]
I multiply both sides by '7' I get:
\[7y = 9x + 25\]


that's^ what you need. -_-

Answer 47

-.- i cant do math

Answer 48

63x+175?

Answer 49

As for the time, I have been waiting for you to reply for almost 25 minutes. And I can't help it either, if I just give out an answer, then I guess the fresh brain you just bought from Walmart will remain fresh all it's life. -.-


WHAT DID YOU DO??
Why did you multiply it by '7' again, I just got rid of the fractions!

Answer 50

ohhh

Answer 51

so u already gave me the answer?

Answer 52

@seashell you are not weak at maths, or can't do it, you just lack confidence and the belief that you can do it. The day you get rid of this fear, you will start loving maths. believe me ;)

Answer 53

yeah, that "7x = 9y + 25" is the answer.

Now be honest, did you understand what we did here, or is your mind still in a tailspin?

Answer 54

both

Answer 55

Ohkay, great! Atleast you understood! :D

take a break to calm your mind. :P

Answer 56

kay:D