Question

confused plz help..
Water freezes at 0degrees Celsius and 32degrees Fahrenheit. Water boils at 100degrees Celsius and 212degrees Fahrenheit.


a. Write degrees Celsius as a linear function of degrees Fahrenheit

b. What is the slope of your linear equation? What does it mean?

c. What is the y-intercept and what does it mean?

Answer 1

a linear function
when you see those words think "line" as in y= mx+b
notice that y depends on x. (to get y's value, you sub in a value for x and do the arithmetic)

so part (a)
Celsius as a linear function of degrees Fahrenheit
means treat Celsius as y ( it depends on Fahrenheit) and Fahrenheit as x

You have two (x,y) points: (32,0) and (212,100)
can you find the equation of a line through two points?
at the end, relabel x as F and y as C

Answer 2

so I graph (32,0) and (212,100)?

Answer 3

the question is asking for an equation. Normally you would use the 2 point formula, or you could first find the slope (change in y divided by change in x)
and then use
y-y1 = m(x-x1) where (x1,y1) is one of the points they give you.

Answer 4

so it would be 100-32= m(212-0)

Answer 5

almost. First find the slope.

Answer 6

how do u do that?

Answer 7

when you have time watch
http://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/v/point-slope-and-standard-form
and
http://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/v/slope-of-a-line

but slope is the difference between the 2 y values (subtract them) divided by the difference in the x values)

Answer 8

oh ok i will

thank u i think i got it from here :)

Answer 9

@phi the slope is 5/9

Answer 10

yes.

Answer 11

for (a) you want y= 5/9 x + b
you need to find b
one way is replace x and y from one of the points (pick the one with zero, it's easier)

Answer 12

ok i will do that right now

Answer 13

so I replace x and y with zero and do the problem?

Answer 14

replace (x,y) with (32,0) x=32 y=0

Answer 15

oh ok

Answer 16

0=160/9+b
then do i -160/9 from both sides?

Answer 17

yes

Answer 18

160/9=b

17.7=b

Answer 19

-160/9

-17.7*

Answer 20

ok, except I would leave it as -160/9 (it makes the equation exact)

Answer 21

oh ok thank u :)

what do i do for c? i dont understand what im supposed to do

Answer 22

first, what did you get for (a)?

Answer 23

a. i got -160/9 right? or was there more to it?

Answer 24

-160/9 is b
you want to whole equation y= mx+b
for (a)

Answer 25

how do you solve for that ... like this?

100=5/9(212)+(-160/90

Answer 26

(-160/9)*

Answer 27

that will be true. but all (x,y) pairs will be true. make y and x variables in the equation

Answer 28

the whole point is we want an equation where you put in an x, and the equation tells you how to find y.

Answer 29

y=5/9(212)+(-160/9)

Answer 30

close. but the 212 should be x

you get
y= (5/9)x -160/9

now if you put x= 212, you can find y: 5*212/9 -160/9= 100 . We find 212 F = 100 C!

Answer 31

So for (a) I would replace x and y with F and C, so it's easier to understand:

C= (5/9)F - 160/9

Answer 32

100=(5/9)(212)-160/9


so the y-intercept is c? which is 100

Answer 33

Better go watch the videos (search for y intercept). But in the equation
y= mx+b m is the slope and b is the y-intercept.
for this equation
y= (5/9)x - 160/9 m= 5/9 and b (the y-intercept) is -160/9

Answer 34

so (b) the slop = 5/9. It means that 1 degree change in Fahrenheit is only 5/9 of a degree change in Celsius. (Fahrenheit degrees are smaller)

Answer 35

oh ok b=y-intercept

Answer 36

for (c)
the y-intercept is -160/9 or about -17.8
this means that when it is 0 F it is -17.8 C or about -18 C when 0 F

Answer 37

oh ok b=y-intercept

that is why they call y= mx+b "slope intercept form" m =slope, b =y-intercept

Answer 38

oh i see now
thank you for all of your help! :) ill go watch the videos now!

Answer 39

They are pretty good if you have enough popcorn.

Answer 40

lol awesome