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
Sales total increases 43,000/20 = 2150 per month.
You don't say whether this is monthly sales or cumulative sales.
If m is the month number and S the total sales,
S = 22,850 + 2150*(m-2)
= 2150 m + 18,550
To find the equation for the line that represents the total sales as a function of time, we can use the two given data points.
We have two data points: (3, 25000) and (23, 68000). The first number in each pair represents the number of months, and the second number represents the total sales.
We can use the slope-intercept form, y = mx + b, where y represents the total sales, x represents the number of months, m represents the slope, and b represents the y-intercept.
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (68000 - 25000) / (23 - 3)
m = 43000 / 20
m = 2150
Now that we have the slope, we can find the y-intercept (b) by substituting one of the data points and the slope into the slope-intercept form.
Using the first data point (3 months, $25,000):
25000 = (2150 * 3) + b
25000 = 6450 + b
b = 25000 - 6450
b = 18550
So the equation for the line is:
y = 2150x + 18550
To predict the total sales after 40 months, we can substitute x = 40 into the equation:
y = 2150 * 40 + 18550
y = 86000 + 18550
y = $104,550
Therefore, the predicted total sales after 40 months is $104,550.