Question

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

Answer 1

see the explanation

Explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
`k=(y)/(x)` or
`y=kx`

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

`k=(y)/(x)`

For x=2, y=25 --->
`k=(25)/(2)=12.5`

For x=4, y=50 --->
`k=(50)/(4)=12.5`

For x=6, y=75 --->
`k=(75)/(6)=12.5`

For x=8, y=100 --->
`k=(100)/(8)=12.5`

so

The value of k is
`12.5\ (m)/(sec)`

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

The linear equation is equal to

`y=12.5x`

or

`Distance=12.5Time`