Question

find the constant of proportionality and the unit rate for the data in the table then write an equation to represent the relation ship between time t an distance d

Answer 1

where is table

Answer 2

I think that the proportionality constant and the unit rate are the same quantity. In order to get such unit rate, please note that, if we compute the ratio between the distance and the corresponding time, we get
\[\Large \frac{{270}}{6} = \frac{{225}}{5} = \frac{{135}}{3} = \frac{{90}}{2} = ...?\]
please what is the value of such common ratio?

Answer 3

0/1?

Answer 4

hint:
what is \(90/2=...?\)

Answer 5

is \(90/2=45\)?

Answer 6

so what is answer

Answer 7

please note that I can not give direct answers, since it is against the Code of Conduct

Answer 8

so i would be 45

Answer 9

yes! that's right!

Answer 10

we have: \(45 \cdot 3=135\), \(45 \cdot 5=225\), and \(45 \cdot 6=270\)

Answer 11

therefore for a generic distance \(d\) and for a generic time \(t\), we can write:
\[\huge \frac{d}{t} = 45\]
Now, please if I multiply both sides of such equation by \(t\), I get:
\[\huge \frac{d}{t} \cdot t = 45 \cdot t\]
please simplify such equation, what do you get?

Answer 12

hint:

Answer 13

45

Answer 14

we have:
\[\huge \frac{d}{t} \cdot t = d\]
am I right?

Answer 15

yes

Answer 16

well idk

Answer 17

so, after such simplification, we can write:
\[\huge d = 45 \cdot t\]
which is the requested relation between distance and time

Answer 18

and we have solved your exercise! :)