Question

What is the equation of the line that passes through the points (-1, 3) and (1, 11)?

4x - y = 1

4x + y = 1

x - 4y = -13

4x - y = -7

Answer 1

any ideas?
first you need the slope

Answer 2

What's the formula for finding the slope?

Answer 3

change in \(y\) over the change in \(x\)

Answer 4

sometimes written \(\frac{y_2-y_1}{x_2-x_1}\)

Answer 5

Oh yeah. Okay give me a second to to this.

Answer 6

ok

Answer 7

I got 4.

Answer 8

ok good

Answer 9

Now what is the next step?

Answer 10

you have a choice
you can use the point-slope formula to find the equation of the line, or since you only have 4 choices you can pick the one that has slope of 4
in fact we should probably use the first method,
\[y-y_1=m(x-x_1)\]

Answer 11

How would I set that up?

Answer 12

oh in fact we have to use the first method, since there are two lines with slope 4
make the number replacements in the formula
\[y-y_1=m(x-x_1)\] with \(x_1=1,y_1=11, m=4\)

Answer 13

you should get
\[y-11=4(x-1)\]

Answer 14

>.< Ah, I hate this part.

Answer 15

yeah i know, but the steps are always the same

Answer 16

just like yesterday

Answer 17

So minus the 1 from 11?

Answer 18

multiply out using the distributive law to get
\[y-11=4x-4\] no distribute first
that is always the first step

Answer 19

Oh yeah. Okay so.
y-11=4x-4

Answer 20

\[(y-11)/(x-1)=(11-3)/(1+1)\]
\[(y-11)/(x-1)=4\]
\[4x-y=-7\]

Answer 21

make sure to use the distributive law to get rid of the parentheses

Answer 22

then you can add 11 to both sides
\[y=4x+7\]

Answer 23

?

Answer 24

we had
\[y-11=4x-4\] and now we want to write it in standard form

Answer 25

first we can add 11 to both sides to get
\[y=4x+7\] is that ok?

Answer 26

So then we would get 4x - y = -7?

Answer 27

this is the "slope intercept" form from last night

Answer 28

then we can put all the variables on one side, the number on the other

Answer 29

Oh I see.
I'm very slow at learning. Takes me a million times to do something before it's pinned in my small brain for good.

Answer 30

subtract \(y\) from both sides and subtract 7 from both sides and get the answer you wrote

Answer 31

of course it takes practice. you were not born knowing this

Answer 32

but the steps are always the same so if you do several it will become easier

Answer 33

we can try another if you like

Answer 34

Thanks for your help (:
We can practice some tomorrow.
I'm doing a practice assignment that is due soon.

Answer 35

good luck