Answer:
a) y = -19/44t +62; y = 5/11t +29
b) 2007
Step-by-step explanation:
(a) The two-point form of the equation of a line is useful when two data points are given.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
Middle Income
The two given points are (0, 62), (44, 43), so the equation is ...
y = (43 -62)/(44 -0)(t -0) +62
y = -19/44t +62
__
Upper Income
The two given points are (0, 29), (44, 49), so the equation is ...
y = (49 -29)/(44 -0)(t -0) +29
y = 20/44t +29
y = 5/11t +29
__
(b) The year in which the shares are equal is found by setting the y-values equal:
-19/44t +62 = 5/11t +29
33 = 39/44t
t = (33)(44)/39 ≈ 37.2
The upper income share exceeded the middle income share in the year 1970 +37.2 = 2007.