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Question 1152200: Assume that in 2013 the number of vehicle sales in the Ukraine was 233 thousand and in 2018 it was 96 thousand.
a. Determine the average rate of change (slope) in the number of vehicle sales from 2013 to 2018. Include
the units. (What does the answer mean?)
b. If x is the number of years since 2013 and g(x) is the number of vehicles sold, write the equation of the
line through these two points.
c. Assuming g(x) is a linear function, use the equation to predict the number of vehicles sold in 2020.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 2018 minus 2013 = 5
96 minus 233 = -137
two points are (x1,y1) = (0,233) and (x2,y2) = 5,
slope is (y2 - y1) / (x2 - x1) = (96 - 233) / (5 - 0) = -137 / 5
slope intercept form of straight line equation is y = mx + b
m is the slope
b is the y-intercept.
since your slope is -137 / 5, then y = mx + b becomes y = -137 / 5 * x + b
to solve for b, replace x and y with one of the points.
i chose (x2,y2) = (5,96)
equation becomes 96 = -137 / 5 * 5 + b
simplify to get 96 = -137 + b
solve for b to get b = 137 + 96 = 233
the equation becomes y = -137 / 5 * x + 233
when x = 0, the year is 2013
when x = 1, the year is 2014
when x = 2, the year is 2015
when x = 3, the year is 2016
when x = 4, the year is 2017
when x = 5, the year is 2018
the equation can be called g(x) = -137 / 5 * x + 233 when you let y = g(x)
the year 2020 is 2 years more than 2018, therefore x = 7 represents 2020.
when x = 7, the equation becomes y = g(x) = -137 / 5 * 7 + 233 = 41.2.
that means that 41.2 thousand vehicles are predicted to be sold in the ukraine in 2020 if the straight line trend continues as represented by the equation.
here's the graph.
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