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

Answer:

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 $k=\frac{y}{x}$ 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

$k=\frac{y}{x}$

For x=2, y=25 ---> $k=\frac{25}{2}=12.5$

For x=4, y=50 ---> $k=\frac{50}{4}=12.5$

For x=6, y=75 ---> $k=\frac{75}{6}=12.5$

For x=8, y=100 ---> $k=\frac{100}{8}=12.5$

so

The value of k is $12.5\ \frac{m}{sec}$

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

$Distance=12.5Time$