Question

Find the equation (in terms of x) of the line through the points (-4,3) and (2,1)

Answer 1

So, what's the slope formula?

Answer 2

y=mx+b is that the correct one or is it asking you y= y2-y1/x2-x1?

Answer 3

the second one

Answer 4

very good, ok, so do you know how to calculate the slope? (find m)

Answer 5

i just use the formula( plug i n the points) and my answer is m,
is that correct? if not can you tell me the right way?

Answer 6

Oh and it's m not y. \[m=\frac{ y_2-y_1}{x_2-x_1}\]

Answer 7

And yep, so what is your y1?

Answer 8

give me one moment and ill work it out

Answer 9

or just show the work and I can check it

Answer 10

I need you to show your steps so I can make sure you did it right, ok?

Answer 11

okay

Answer 12

[m=1-3\div2-(-4)\]

Answer 13

m=1-3/2-(-4)

Answer 14

-2/6=-0.333
is this correct?

Answer 15

very good, now remember you can't just plug that into a calculator like that

Answer 16

yep yep

Answer 17

so, let's just reduce that fraction

Answer 18

i did 1-3 first then2--4
then i divided the outcomes or -2/6

Answer 19

what can you divide both 2 and 6 by evenly?

Answer 20

That's perfect

Answer 21

1/3?

Answer 22

ok good, so it still stays negative though

Answer 23

okay so the final answer would be -1/3 ?

Answer 24

that's the m (slope)

Answer 25

we still have to come up with an equation

Answer 26

since its asking for the equation, how should i go about that?

Answer 27

y=1/3x+b
do i need to come up with the b?

Answer 28

So two ways, 1: you were given something called point slope form
2: we do the quick derivation

Answer 29

3: you graph it and hope your y intercept is a nice number

Answer 30

um can you help me with whatever one you think is best?
im not sure how to do any tbh.
what do i graph?

Answer 31

ok, so let's do the very quick derivation, just so you get to see it

Answer 32

So before, you told me that we find slope by \[m=\frac{y_2-y_1}{x_2-x_1}\]
So if we wanted to get the ys by themselves, we could multiply both sides by the bottom of the fraction and 'undo' the division.
\[m(x_2-x_1)=\frac{y_2-y_1}{x_2-x_1}*(x_2-x_1)\]
So the right hand side cancels and we get:
\[m(x_2-x_1)=y_2-y_1\]
Since we prefer the y's on the left hand side we flip it,
\[y_2-y_1=m(x_2-x_1)\]
And we drop the sub twos
\[y-y_1=m(x-x_1)\]
We now have point slope form :)

Answer 33

So for point slope form, if you have a point you put it in place of x1 and y1. Then you found m already, so you are all set to simplify