Question

Write the standard form of the equation of the line passing the point. (-1, 4), (3, -2). Explanation? Please :)

Answer 1

Okay, two things we need for a line (most of the time) is a slope, and a point... With two points, you can easily get the slope of the line... do you know how?

Answer 2

To refresh you, if you have two points, (a,b) and (c,d), the slope m of the line is given by...
\[\Large m = \frac{d-b}{c-a}\]Note that it doesn't matter if you have it as...
\[\Large m = \frac{b-d}{a-c}= \frac{-1(d-b)}{-1(c-a)}= \frac{d-b}{c-a}\]
Just be careful... and CONSISTENT :)

Answer 3

Oh my, I'm sure I do, but I can't remember how. This was taught the beginning of the semester, It's a question on my finals. Does it have to do with subtracting the x and y values?

Answer 4

It has everything to do with subtracting x and y values :)
Basically, the slope equals the change in y divided by the change in x... denoted
\[\Large m= \frac{\Delta y}{\Delta x}\]

Answer 5

That's not yet the answer, though.... that's just the slope... that said, what IS the slope?

Answer 6

With this equation, it's equal to 1/2. How can standard form most easily be defined as? "Write in standard form. . ."

Answer 7

Nope, it isn't 1/2 at all.... check it again :)

Answer 8

Oh, I'm dumb. Thanks for the patience by the way. . Ahhhhhhh, 1/2 being the slope?

Answer 9

Yeah... 1/2 is not the slope...
(-1 4) and (3 , -2)
remember the formula...
\[\Large m = \frac{d-b}{c-a}\]

Answer 10

And your (a,b) is (-1 , 4)
while (c,d) is (3,-2)

Answer 11

Right. -2-4 is -6. 3+1=4. . . . -2/3?

Answer 12

backwards.... it's the difference of the Y's over the difference of the X's :P

Answer 13

LOL, oh gosh. I feel so dumb. Okay, 3/-2. And from there? y=mx+b?

Answer 14

Yes... we'll get there :D
so you have the slope,
\[\Large m = -\frac32\] right?

Answer 15

Yes. Got it!

Answer 16

So, you now have a slope m, and a point (two of them, in fact)
You pick one of these points (it doesn't really matter which)
Have you picked one? Great.
Now, let that point be (h,k)
The line would be...
\[\Large y = \color{red}m(x-\color{green}h)+ \color{blue}k\]

Answer 17

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

Answer 18

Be attentive...
\[\Large y = m(x\color{red}{-}h) +k\]
That's a MINUS sign there...

Answer 19

Boo! Sorry. Minor changes. . y=-3/2(x+1)+4

Next?

Answer 20

Better :)
\[\LARGE y = -\frac32(x+1) + 4\]
All that's left is to simplify :)

Answer 21

Isn't that in standard form?

Answer 22

Not yet... it has to be in the form
\[\LARGE \color{red}y = \color{green}m \color{blue}x + \color{orange}b\]

Answer 23

So, distribute that -3/2, and then simplify... that's all there is to it :)

Answer 24

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

What is the answer? I can figure it out from there and work back
wards. Lol

Answer 25

You're confusing me... :/
\[\Large y = -\frac32(\color{green}x+\color{green}1)+4\]
I just said distribute the -3/2 over the x and the +1, and then simplify.

Answer 26

That is -3/2x -3/2 + 4?

Answer 27

Okay... good so far :)
\[\Large y = -\frac32x -\frac32 + 4\]Now simplify this part...
\[\Large y = -\frac32x \color{blue}{-\frac32 + 4}\]

Answer 28

y=-3/2x -6

Answer 29

Nope... review your addition and subtraction of fractions :)

Answer 30

What! I was pretty confident. Lol, what is the answer?

Answer 31

Can't tell you that :P
Do it over... c'mon, you can do this, it's just one tiny step more :D

Answer 32

Aww, thanks for the encouragement. Hmm, y=-3/2+4?

Answer 33

What happened to the x?
Come on, it has all boiled down to this...
\[\LARGE -\frac32 + 4 = \color{red}?\]

Answer 34

Lol, my bad. . y=-3/2x + 5 1/2?

Answer 35

Nope... note the minus sign on the "3/2"
Besides, you shouldn't use mixed-number fractions, use improper fractions...

Answer 36

LOL, I am so not feeling this. y=-3/2x -6?

Answer 37

Nope...

Answer 38

OMG. Thanks for your help. Lol, Good Night :)