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?

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  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
    6 = 1 (2) + b
    b = 4
    y = x + 4 (indeed, we could have figured that out with a sketched graph.)
    then if = 7 then y = 7 + 4 = 11

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