The total sales made by a salesperson was $25,000 after 3 months and $68,000 after 23 months. Using an equation for the line whose graph depicts this data, predict the total sales after 40 months.
To predict the total sales after 40 months, we can use linear regression to find the equation of the line that best fits the given data.
Step 1: Determine the slope of the line
The slope of the line can be calculated by using the formula:
slope = (y2 - y1) / (x2 - x1)
Using the given data, substitute the values:
m = (68000 - 25000) / (23 - 3)
m = 43000 / 20
m = 2150
Step 2: Determine the y-intercept of the line
To find the y-intercept (b), substitute the values of one point (x, y) into the equation:
y = mx + b
Using the point (3, 25000), substitute the values:
25000 = 2150 * 3 + b
25000 = 6450 + b
b = 25000 - 6450
b = 18550
Step 3: Write the equation of the line
Now that we have found the slope (m) and the y-intercept (b), we can write the equation of the line:
y = mx + b
y = 2150x + 18550
Step 4: Predict the total sales after 40 months
Substitute the value x = 40 into the equation:
y = 2150 * 40 + 18550
y = 86000 + 18550
y = 104550
Therefore, the predicted total sales after 40 months is $104,550.