Question

What is the slope of the line through points p( 1,2) and q(7,-3)

Answer 1

@zepdrix

Answer 2

I got -6/5

Answer 3

Slope is given by,
\[\Large \frac{\Delta y}{\Delta x} \qquad=\qquad \frac{y_2-y_1}{x_2-x_1}\]

Looks like we were given,\[\Large (x_1,y_1)=(1,2) \qquad\qquad\qquad (x_2,y_2)=(7,-3)\]

Plugging everything in gives us,\[\Large \frac{-3-2}{7-1}\]

Hmmm I think maybe you have it upside down XD

Answer 4

Oh okay! i got it. There is another similar question,

What is the equation of the line with the slope of 3 and through the point 4 , 1

Answer 5

The equation of a line in slope-intercept form is,
\[\Large y=mx+b\]Where the slope is our \(\Large m\)
and the y-intercept is \(\Large b\)

So we can plug the slope value directly in for \(\Large m\).
Then to solve for \(\Large b\), we'll have to plug in the coordinate pair they gave us,\[\Large y=3x+b\]Plug in your \(\large (4,1)\) to find b! :)

Answer 6

What do you mean by plug in? where? @zepdrix

Answer 7

\[\Large (x,y)=(4,1)\]Plug 4 in for x,
1 in for y.

Into this,\[\Large y=3x+b\]

Answer 8

y=12+1

Answer 9

no no wait

Answer 10

1 = 12 + b? @zepdrix

Answer 11

mm ya that looks right, so what do you get for b? solve for b! :O

Answer 12

-11

Answer 13

Ok good.
Now we want to back up a step, leave the (4,1) out of the equation and plug in your m and b to get the final form we're looking for.

Answer 14

y = 3x -11
?

Answer 15

yay good job \c:/

Answer 16

okay one last problem I promise!!

Answer 17

Solve the system of equations


3x + 3y = 6

5x - 6y =15

Answer 18

There are two really convenient methods for solving linear systems like this,
`substitution` and `elimination`.
Do either of those sound familiar? :O

Answer 19

Ive used subsitution in the past, but it wont seem to work right now

Answer 20

It would work, it would just take a few extra steps.
Elimination might be a little easier for this one. :)

Answer 21

We want to match up the coefficients on `one` of our variables in both equations.
In this equation let's try to match up the coefficient on our x's.

After we do that, we can subtract the equations and the x's will cancel out.
That will allow us to solve for y.

Hmm let's multiply this first equation by 5,\[\Large 3x+3y=6 \qquad\to\qquad 15x+15y=30\]

Answer 22

And then we want to multiply our second equation by 3, both sides as we did before,\[\Large 5x-6y=15 \qquad\to\qquad ?\]How bout you do this one ^^

Answer 23

Wait, how do we know what to multiply by

Answer 24

i got it though, 15x -18y = 45

Answer 25

and I understand how we know what to multiply by

Answer 26

Oh you figured that out? :) k cool.

Answer 27

yea, let me see if I can do the rest

Answer 28

\[\Large 15x+15y=30\]\[\Large 15x -18y = 45\]k :)

Answer 29

x = 35/70

Answer 30

i mean 75/30

Answer 31

x = 2.5

Answer 32

you solved for x first?
That's strange :o we wanted to solve for y first.
That's why we matched up the values on x.
So they would cancel out when we subtract the equations.

Answer 33

Oh darn! I knew that... just had a brain fart ):

Answer 34

y = -25

Answer 35

Hmmm not quite :O Let's see...
subtracting the bottom equation from the top one gives us,\[\Large 0x+33y=-15\]

Answer 36

how 33y?

Answer 37

15 - 18

Answer 38

We're subtracting this equation from the other one,
\[\Large 15x -18y = 45\]
So we have to remember that the subtraction applies to EVERY term in this equation,\[\Large -(15x -18y) = -(45)\]

Answer 39

So it becomes a positive 18 when we distribute that negative sign.

Answer 40

why would we distribute a - sign

Answer 41

That's what we do when we subtract multiple terms.
We have to apply the subtraction to each term.
So it flips the sign of everything.

Answer 42

were subtracting? I thought we were adding

Answer 43

\[\Large 15x+15y=30\]\[\Large 15x -18y = 45\]

If we added these equations together, it would give us 30x :[
that's not what we want.
We want to cancel out the x's.

Answer 44

so we multiply each by -

Answer 45

yes :) maybe that's a better way to explain it hehe

Answer 46

so it changes them to

0x -15y = -30
0x +18 = -45

Answer 47

ah woops, i shoulda been more clear :(
we want to multiply `one of the equations` by -1.

Answer 48

so were doing the bottom one? we get

0x + 15y = 30
0x + 18 = -45

Answer 49

The way you wrote those 0's a little strange :) We want to perform all of the addition/subtraction at the same time. But yes it looks good.