The table below shows the distance a train traveled over time. how can you determine the equation that represents this relationship?
time (s) distance (m)
2 25
4 50
6 75
8 100

i don’t understand this

see the explanation

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Let

x ----> the time in seconds

y ---> the distance in meters

In this problem we have a proportional relationship between the variables x and y

Find the constant of proportionality k

For x=2, y=25 --->

For x=4, y=50 --->

For x=6, y=75 --->

For x=8, y=100 --->

so

The value of k is

In this problem the value of k or slope represent the speed of the train

The linear equation is equal to

or

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so:

54 km / hours

step-by-step explanation:

we need to convert seconds to hours

60 seconds = 1 minutes

60 minutes = 1hour

15 m         60 second   60 minutes

  * *         = 54000 meters/ hour

second     1 minute             1 hour

now we need to convert meters to km

1000 m = 1 km

54000 m       1 km

*   = 54 km / hours

hour               1000m