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5 cents in 1964. It was 49 cents in 2014.  Using your linear model, find the year in which postage was 37 cents. Round to a whole year.

$\begin{array}{rcl} \dfrac{49-5}{2014-1964} &=& \dfrac{37-5}{y-1964} \\ \dfrac{44}{50} &=& \dfrac{32}{y-1964} \\ y-1964 &=& \dfrac{32\cdot 50}{44} \\ y &=& 1964 + \dfrac{32\cdot 50}{44} \\ y &=& 1964 + 36.\overline{36}\\ y &=& 2000.\overline{36}\\ \mathbf{y} & \mathbf{=} & \mathbf{2000}\\ \end{array}$

The year in whitch postage was 37 cents was 2000

5 cents in 1964. It was 49 cents in 2014.  Using your linear model, find the year in which postage was 37 cents. Round to a whole year.

Let 1964=year0      so  2014=year  50

y=m*x +5

49=m*50+5

44=50m

m=44/50 = 88/100 = 0.88

so

y=0.88x+5

Find x when y=37

37=0.88x+5

32=0.88x

x=32/0.88 = 36   to the nearest whole.

1964+36 = 2000

So if the linear model is accurate then the price was 37c in the year 2000.