Question

what is the equation of the line that goes through (1,3) and (5,12) ?

Answer 1

equation of the line y=mx+b    this line  goes through (1,3) and (5,12)
so    3=m*1+b
and 12=m*5+b
solve the system of equations $\left \{ {{3=m+b} \atop {12=5m+b}} \right.$

second equation minus first is:
12-3=5m+b-m-b
9=4m
m=9/4
m=2.25

3=m+b
3=2.25+b
b=0.75

equation of the line y=mx+b
y=2.25x+0.75
Answer:  equation of the line  is y=2.25x+0.75

Answer 2

m = y₂ - y₁ = 12 - 3 = 9 = 2.25
       x₂ - x₁      5 - 1    4