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 [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
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
[tex]k=\frac{y}{x}[/tex]
For x=2, y=25 ---> [tex]k=\frac{25}{2}=12.5[/tex]
For x=4, y=50 ---> [tex]k=\frac{50}{4}=12.5[/tex]
For x=6, y=75 ---> [tex]k=\frac{75}{6}=12.5[/tex]
For x=8, y=100 ---> [tex]k=\frac{100}{8}=12.5[/tex]
so
The value of k is [tex]12.5\ \frac{m}{sec}[/tex]
In this problem the value of k or slope represent the speed of the train
The linear equation is equal to
[tex]y=12.5x[/tex]
or
[tex]Distance=12.5Time[/tex]
