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Sales of automobiles worldwide continue to grow as emerging economies provide their citizens more purchasing power. In 2010, there were 56 thousand new car sales in a region, and in 2014, this number increased to 68 thousand cars. Assume that the relationship between time, \(x\), and the number of new cars sold, \(y\), is a linear relationship.

a. Write an equation describing the relationship between time and the number of new automobiles sold in the region. Use ordered pairs of the form (years past 2010, number of automobiles sold).

b. Use this equation to predict the number of new car sales in the region in the year 2019.

a. The equation describing the relationship is (Type your answer in slope-intercept form.)

Answer :

According to the equation, we can predict that there would be around 83 thousand new car sales in the region in the year 2019.

The equation describing the relationship between time (x) and the number of new automobiles sold (y) in the region is in slope-intercept form, y = mx + b.

To find the equation, we can use the two given data points: (0, 56) and (4, 68). These points represent the years past 2010 and the corresponding number of automobiles sold.

Using the formula, we can calculate the slope (m) of the line:

m = (y2 - y1) / (x2 - x1)
m = (68 - 56) / (4 - 0)
m = 12 / 4
m = 3

Now, let's substitute one of the points and the slope into the slope-intercept form to find the y-intercept (b):

56 = 3(0) + b
b = 56

Therefore, the equation describing the relationship is:
y = 3x + 56

Now, to predict the number of new car sales in the region in the year 2019, we need to substitute the year (x = 9) into the equation:

y = 3(9) + 56
y = 27 + 56
y = 83

Know more about the slope-intercept form,

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