What is the equation of a line that passes through the points (0,5) and (4,8)?

A linear function has the form y=mx+b
if you insert the point (0,5) in this you receive:
5=m*0+b
5=b
(remember b is the distance to the x axis at x=0, so you can read it directly of)

To get m you insert (4,8) and the previous b:
8=m*4+5
3=4m
3/4=m

your line is: y=3/4x+5

(also this question is a duplicate of #3469085 by you :) )