Question

write a rule for the linear function in the table.
Please can someone help me understand?

Answer 1

is a "linear function"

meaning, it makes a line

so let us pick 2 points from the table first, say the 1st and last
keep in mind that we could really pick any two points off the set \( \begin{array}{ccllll}
x&y
\\\hline\\
\underline{-4}&\underline{16}\\
0&0\\
4&-16\\
\underline{8}&-\underline{32}
\end{array}
\\ \quad \\ \bf
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ -4}}\quad ,&{\color{blue}{ 16}})\quad &({\color{red}{ 8}}\quad ,&{\color{blue}{ -32}})
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies \cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}
\\ \quad \\

y-{\color{blue}{ y_1}}={\color{green}{ m}}(x-{\color{red}{ x_1}})\qquad \textit{plug in the values and solve for "y"}\\
\qquad \uparrow\\
\textit{point-slope form}\)

Answer 2

so you'd get the slope, and plug in your values in the "point-slope form"

then you can solve it for "y" if you need it in slope-intercept form
if you do not, they you can leave it like so, in point-slope form too

Answer 3

do you understand what jdoe posted?

they want you to find the equation of line that goes through those points

do you know how to find the equation of a line?

Answer 4

Oh okay let me try it

Answer 5

pick two points and find the slope between those two points

I would use (0,0) as one of the points (easy math)

Answer 6

For future reference, here is a video about slope
http://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/slope-and-intercepts/v/slope-of-a-line

Answer 7

I got 12/36

Answer 8

what two points did you use?

Answer 9

I used -2/5 then 3/3

Answer 10

wait i got it mix up

Answer 11

-4-8 = 12 then the second one is 16-32=36
then I divided into 2where it came out to 6/16

Answer 12

is that correct or am I missing something?

Answer 13

so you used the first point (-4,16) and the last point (8,-32)

the x values are the first number in each pair.
the y values are the second number in each pair.

change in y is 16 - (-32)
change in x is -4 - 8

can you simplify those?

Answer 14

you could use a calculator if you have one.

Answer 15

Okay let me try

Answer 16

48/12 simplify that?

Answer 17

almost. -4 - 8 is not +12
try again

Answer 18

so is minus?

Answer 19

yes. try it with a calculator (but I would learn how to do negative numbers!)

you get 48/-12
which simplifies to -4

Answer 20

oh okay how would I used the negative on the calculator

let me check on that link

Answer 21

so the answer fCX) -4x?

Answer 22

f(x)= -4x

the way you get that is to know the equation of a line is
f(x) = mx + b
where m is the slope (some number) and b is the y-intercept.

we found the slope to be -4, (i.e. m= -4) so we know (so far)

f(x)= -4x + b

to find b, we pick a point that is on the line (in the table)
I would pick (0,0) (but any pair will work)

replace x with 0, and replace f(x) with 0 in our equation to get
0 = -4*0 + b
simplify : 0= 0+b
b+0 is b (adding 0 to anything , even a letter, does not change it)
we get 0 = b
so we know b is 0 and the equation is
f(x)= -4 x + 0

but we never bother to write +0 , so we just write
f(x)= -4 x

Answer 23

thank you so much!!!!!

Answer 24

yw