Linear equation
This relationship can be modeled using the linear equation given by
y = mx +b, where m and b are numbers
We know m is the rate of change of y with respect to x
In order to determine m we select two points, in this case we are selecting first and second column, we have that
x₁ = 2 and y₁ = 6
x₂ = 4 and y₂ = 12
then the change of x and y is given by
Δx = x₂ - x₁ = 4 - 2
Δx = 2
Δy = y₂ - y₁ = 12 - 6
Δy = 6
We know
m = Δy / Δx = 6 / 3
then m = 3
Then, replacing m in the first equation:
y = 3x + b
We just need to find b. Selecting any point, we replace x and y value:
y₁ = 3x₁ + b
6 = 3 · 2 + b
6 = 6 + b
6 - 6 = b
Then, b = 0
Then the equation that models it is y = 3x