Write An Equation, In Slope-intercept Form, That Represents The Total Amount, { Y $}$, In Dollars, Of Mr. Jensen's Paycheck In A Month When He Sells { X $}$ Policies. His Monthly Paycheck Includes A Base Salary Of [$ $2,175
Introduction
In this article, we will delve into the world of mathematics to understand the relationship between Mr. Jensen's paycheck and the number of policies he sells. We will create an equation in slope-intercept form that represents the total amount of his paycheck in a month.
The Problem
Mr. Jensen's monthly paycheck includes a base salary of $2,175 and a commission of $100 for each policy he sells. We need to find an equation that represents the total amount of his paycheck in a month when he sells x policies.
The Equation
Let's start by identifying the variables and constants in the problem.
- x: The number of policies Mr. Jensen sells in a month.
- y: The total amount of Mr. Jensen's paycheck in a month.
- 2,175: The base salary Mr. Jensen receives every month.
- 100: The commission Mr. Jensen receives for each policy he sells.
The equation we are looking for is in slope-intercept form, which is given by:
y = mx + b
where m is the slope of the line and b is the y-intercept.
In this case, the slope m represents the commission Mr. Jensen receives for each policy he sells, which is $100. The y-intercept b represents the base salary Mr. Jensen receives every month, which is $2,175.
Therefore, the equation that represents the total amount of Mr. Jensen's paycheck in a month when he sells x policies is:
y = 100x + 2175
Interpretation of the Equation
Let's break down the equation and understand what it represents.
- y = 100x: This part of the equation represents the commission Mr. Jensen receives for each policy he sells. The slope m is 100, which means that for every additional policy Mr. Jensen sells, his paycheck increases by $100.
- + 2175: This part of the equation represents the base salary Mr. Jensen receives every month. The y-intercept b is 2175, which means that Mr. Jensen receives a base salary of $2,175 regardless of the number of policies he sells.
Example
Let's use the equation to find the total amount of Mr. Jensen's paycheck in a month when he sells 10 policies.
y = 100x + 2175
y = 100(10) + 2175
y = 1000 + 2175
y = 3175
Therefore, the total amount of Mr. Jensen's paycheck in a month when he sells 10 policies is $3,175.
Conclusion
In this article, we created an equation in slope-intercept form that represents the total amount of Mr. Jensen's paycheck in a month when he sells x policies. The equation is given by:
y = 100x + 2175
We interpreted the equation and understood what it represents. We also used the equation to find the total amount of Mr. Jensen's paycheck in a month when he sells 10 policies.
References
- [1] Algebra I. (n.d.). Retrieved from https://.khanacademy.org/math/algebra
- [2] Slope-Intercept Form. (n.d.). Retrieved from https://www.mathway.com/questions/linear-equations/slope-intercept-form
Frequently Asked Questions
Q: What is the base salary of Mr. Jensen?
A: The base salary of Mr. Jensen is $2,175.
Q: What is the commission Mr. Jensen receives for each policy he sells?
A: The commission Mr. Jensen receives for each policy he sells is $100.
Q: What is the equation that represents the total amount of Mr. Jensen's paycheck in a month when he sells x policies?
A: The equation that represents the total amount of Mr. Jensen's paycheck in a month when he sells x policies is:
y = 100x + 2175
Q: How do I use the equation to find the total amount of Mr. Jensen's paycheck in a month when he sells a certain number of policies?
Q: What is the base salary of Mr. Jensen?
A: The base salary of Mr. Jensen is $2,175. This is the amount he receives every month regardless of the number of policies he sells.
Q: What is the commission Mr. Jensen receives for each policy he sells?
A: The commission Mr. Jensen receives for each policy he sells is $100. This means that for every additional policy he sells, his paycheck increases by $100.
Q: What is the equation that represents the total amount of Mr. Jensen's paycheck in a month when he sells x policies?
A: The equation that represents the total amount of Mr. Jensen's paycheck in a month when he sells x policies is:
y = 100x + 2175
Q: How do I use the equation to find the total amount of Mr. Jensen's paycheck in a month when he sells a certain number of policies?
A: To use the equation, simply substitute the number of policies Mr. Jensen sells into the equation and solve for y. For example, if Mr. Jensen sells 10 policies, you would substitute x = 10 into the equation and solve for y.
Q: What is the total amount of Mr. Jensen's paycheck in a month when he sells 10 policies?
A: To find the total amount of Mr. Jensen's paycheck in a month when he sells 10 policies, we substitute x = 10 into the equation and solve for y.
y = 100x + 2175
y = 100(10) + 2175
y = 1000 + 2175
y = 3175
Therefore, the total amount of Mr. Jensen's paycheck in a month when he sells 10 policies is $3,175.
Q: What is the total amount of Mr. Jensen's paycheck in a month when he sells 20 policies?
A: To find the total amount of Mr. Jensen's paycheck in a month when he sells 20 policies, we substitute x = 20 into the equation and solve for y.
y = 100x + 2175
y = 100(20) + 2175
y = 2000 + 2175
y = 4175
Therefore, the total amount of Mr. Jensen's paycheck in a month when he sells 20 policies is $4,175.
Q: How does the equation change if Mr. Jensen's commission increases to $150 per policy?
A: If Mr. Jensen's commission increases to $150 per policy, the equation would change to:
y = 150x + 2175
This means that for every additional policy Mr. Jensen sells, his paycheck increases by $150.
Q: How does the equation change if Mr. Jensen's base salary increases to $2,500 per month?
A: If Mr. Jensen's base salary increases to $2,500 per month, the equation would change to:
y = 100x + 2500
This means that Mr. Jensen's base salary is now2,500 per month, and he still receives a commission of $100 per policy.
Conclusion
In this article, we answered some frequently asked questions about Mr. Jensen's paycheck. We explained how to use the equation to find the total amount of Mr. Jensen's paycheck in a month when he sells a certain number of policies. We also showed how the equation changes if Mr. Jensen's commission or base salary increases.