Question

Please help! I will give you a medal. :))

A student is running a 10-kilometer race. He runs 1 kilometer every 4 minutes. Select the function that describes his distance from the finish line.

f(x) = - 1 over 4x + 4

f(x) = - 1 over 10x + 4

f(x) = - 1 over 10x + 10

f(x) = - 1 over 4x + 10

Answer 1

if x is the time that has elapsed, then what should f(x) equal when x = 0?

Answer 2

Um... 0?

Answer 3

in other words, how far from the finish line should you be when the time is x = 0 seconds?

Answer 4

Um... not distance from the finish line at all? :S

Answer 5

hint: it's in the first sentence

Answer 6

at the start of the race, you are _____ km from the finish line

Answer 7

So he's 10 km from the finish line? So which function is that? :o

Answer 8

because we know that f(x) = 10 when x = 0, we know that the y-intercept is 10

Answer 9

so we go from y = mx+b to y = mx + 10

Answer 10

how would you use the other given info to determine the slope? any ideas?

Answer 11

I don't know. D:

Answer 12

He runs 1 kilometer every 4 minutes

so as x increases by 4, y decreases by 1

in other words

rise = -1
run = 4

so the slope is ????

Answer 13

umm... oh god this is stressful... umm

Answer 14

lemme just try and do the math real quick i guess

Answer 15

hint: slope = rise/run

Answer 16

So... -0.25?? :o

Answer 17

keep it as a fraction though

Answer 18

what is -0.25 as a fraction??

Answer 19

oh nvm. -1/4 ?? right?

Answer 20

correct, so the function is

\[\large f(x) = -\frac{1}{4}x + 10\]

Answer 21

Ohh! Okay! The slope tip really helped~
Thanks! :DD

Answer 22

you're welcome