Question

Sandy is observing the velocity of a runner at different times. After one hour, the velocity of the runner is 4 km/h. After two hours, the velocity of the runner is 2 km/h.

Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the runner at different times. Show your work and define the variables used. (5 points)

Part B: How can you graph the equations obtained in Part A for the first 4 hours? (5 points)

Answer 1

@Angle

Answer 2

Ok so standard form is ax + by = c right?

Answer 3

yes..

Answer 4

do you have any ideas on how to make the given information into any type of equation? it doesn't have to be the type they suggested for now

Answer 5

for example, the slope intercept form: y = mx + b
or the point-slope form: y = a(x - h) + k ?

Answer 6

nope not really the velocity and the fact its km its just confusing to me

Answer 7

mm yeah, it's a lot of words and a lot of extra information
I don't think we need to pay that much attention to the units, because 4 km/h and 2 km/h is using the same[i/] units

Answer 8

whoops, formatted wrong

Answer 9

in any case
the information we need to use to get equations is:

at hour 1, they went at a speed of 4
at hour 2, they went at a speed of 2

Answer 10

yeah alright

Answer 11

ok...

Answer 12

so the idea is that
y = m(x - h) + k

m = slope
(h, k) = (x, y) point on the line

Answer 13

slope is: "how much does it go up or down, if you move to the right 1 unit"?

in this case, we are going from 4 to 2 if we move to the right by one spot

Answer 14

yes

Answer 15

so what do you think the slope is?

Answer 16

(1,-3)

Answer 17

hmmm let's try this this way

slope = \(\large \frac{d - e}{f - g}\)
\(d = 2\)
\(e = 4\)
\(f = 2\)
\(g = 1\)

Answer 18

2-4 over 2-1

Answer 19

mhm and that can be simplified to?

Answer 20

-1 idk that kinda confused me

Answer 21

\(\large \frac{2-4}{2-1} = \frac{-2}{1} = -2\)

Answer 22

oh

Answer 23

ohh i was going down 3 im silly

Answer 24

"y = m(x - h) + k

m = slope
(h, k) = (x, y) point on the line"

so
m = slope = -2

then a point on the line is (1, 4)


plug this all in and:
y = (-2)*(x - 1) + 4

Answer 25

oh

Answer 26

so wait then for the way they are asking would a good equation be y = –2x + 6

Answer 27

close!
they want it in "standard form"
so the x and y variables on the same side

Answer 28

>just add 2x to both sides to move it

Answer 29

hm

Answer 30

so we want it to look like this

2x + y = 6

Answer 31

right

Answer 32

so that's part 1

Answer 33

*part A

Answer 34

yep now to show how to graph is

Answer 35

it

Answer 36

I graphed part of it, you just need to extend it to include hours 3 and 4

Answer 37

i think i got it

Answer 38

great :)

Answer 39

thank you so much