Suppose that y is a linear function of x, and that y = 6 when x = 2 and y = 7 when x = 3. What is y when x = 7?

Answer 1

(2,6) and (3,7)
slope = (7-6)/(3-2) = 1
so if y = m x + b and m = 1 then
y = 1 x + b
now put in a point, any point
like
6 = 1 (2) + b
so
b = 4
and
y = x + 4 (indeed, we could have figured that out with a sketched graph.)
then if = 7 then y = 7 + 4 = 11