Solve. Assume the exercise describes a linear relationship. When writing a linear equation, write the equation in
slope-intercept form.
-The total sales made by a salesperson was $25,000 after 3 months and $68,000 after 23 months. Predict the total sales after 46 months.
A)$117,492
B)$117,420
C)$117,550
D)$117,450

Question

Quizplus · Accepted Answer

We can start by finding the slope of the linear relationship:

slope = (change in y)/(change in x) = ($68,000 - $25,000)/(23 - 3) = $43,000/20 months = $2,150/month

Now we can use the slope-intercept form of a linear equation to write an equation that relates the total sales (y) to the number of months (x):

y = mx + b

where m is the slope we just calculated, and b is the y-intercept (the starting point of the salesperson's total sales). To find b, we can use one of the given data points, say (3, $25,000):

$25,000 = ($2,150/month)(3 months) + b
b = $25,000 - $6,450 = $18,550

So our linear equation is:

y = ($2,150/month)x + $18,550

To predict the total sales after 46 months, we plug in x = 46:

y = ($2,150/month)(46 months) + $18,550 = $117,450

Therefore, the answer is D, $117,450.

Solve Assume the Exercise Describes a Linear Relationship