Point-slope form: We need a point (x₀,y₀) and the slope (m)
y-y₀=m(x-x₀)
In this case:
y=k
x=t
then:
k-k₀=m(t-t₀)
We know two points (18, 2) and (54,6).
Given two points (x₁,y₁) and (x₂,y₂) the slope of the line passes through these points will be:
m=(y₂-y₁)/(x₂-x₁)
In this case:
m=(6-2)/(54-18)=4/36=1/9
Therefore, we can make up the equation of this line (point-slope form) , we can choose any point of this line (18,2) or (54,6); the result will be the same.
We choose the point (18,2)
k-k₀=m(t-t₀)
k-2=1/9(t-18)
Answer: k-2=1/9(t-18)
