First, we will notice that while the value of x increases by 1, the corresponding value of y increases by 4. This means that this is a linear relation.
The general equation for linear equations is : y = mx + c where m is the slope and c is the y-intercept
To get the slope, we will need to use two points. Let's take the first and the last points: (1,0) and (4,12)
The slope is calculated as: (y2-y1) / (x2-x1)
Use the chosen points to substitute in the equation and get the slope as follows:
m = (12-0) / (4-1) = 12/3 = 4
Now, the equation of the line became: y = 4x + c
The given points all satisfy the equation of the line, we can use any of them to substitute in the equation and get the value of c.
For instance, I will use the first point: (1,0)
y = 4x + c
0 = 4(1) + c
c = -4
The equation of the line is:
y = 4x - 4