Question

Karl Roberts, CEO of Arko Equipment, analyzes the sales data for the first ten years of his company to make decisions for the company's future. Data is only readily available for some of the years the company has been in business. Find an equation for the line of best fit, and use it to approximate the sales for the company's third year to the nearest dollar amount. [Note: the y-intercept is 1500, and the line passes through (10, 2100).]

Answer 1

The general equation of a line is y = mx + b

Where m is the slope of the line and b is the y-intercept

We know b = 1500. Which also implies that the point (0,b) belongs to the line.

To calculate m, we use the two known points:

m = slope = rise / run = (2100 - 1500) / (10 - 0) = 600 / 10 = 60

Now the equation requested is y = 60x + 1500.

Use x = 3 to get the approximate sales for the third year:

y = $3*60 + $1500 = $180 + $1500 = $1680.