Type The Correct Answer In The Box.Mr. Jensen Is A Salesperson For An Insurance Company. His Monthly Paycheck Includes A Base Salary Of $2,175$ And A Commission Of $250$ For Each Policy He Sells.Write An Equation, In Slope-intercept

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Introduction

In the world of sales, a salesperson's income is often directly tied to their performance. For Mr. Jensen, a salesperson for an insurance company, his monthly paycheck includes a base salary of $2,175 and a commission of $250 for each policy he sells. In this article, we will explore the relationship between Mr. Jensen's salary and commission, and write an equation to represent this relationship in slope-intercept form.

The Relationship Between Salary and Commission

Let's start by analyzing the relationship between Mr. Jensen's salary and commission. We know that his base salary is $2,175, and he earns a commission of $250 for each policy he sells. This means that for every policy he sells, his income increases by $250.

Commission as a Function of Policies Sold

We can represent the commission as a function of the number of policies sold. Let's call the number of policies sold "x". Then, the commission can be represented as:

Commission = 250x

Total Income as a Function of Policies Sold

Now, let's consider the total income, which is the sum of the base salary and the commission. We can represent the total income as a function of the number of policies sold:

Total Income = Base Salary + Commission = 2175 + 250x

Slope-Intercept Form

To write the equation in slope-intercept form, we need to isolate the variable x. We can do this by subtracting 2175 from both sides of the equation:

Total Income - 2175 = 250x

Now, we can divide both sides of the equation by 250 to isolate x:

(x) = (Total Income - 2175) / 250

This is the equation in slope-intercept form, where the slope is 250 and the y-intercept is -2175.

Interpretation of the Equation

The equation represents the relationship between Mr. Jensen's total income and the number of policies he sells. The slope of 250 represents the commission earned per policy sold, and the y-intercept of -2175 represents the base salary.

Example

Let's say Mr. Jensen sells 5 policies in a month. We can plug this value into the equation to find his total income:

Total Income = 2175 + 250(5) = 2175 + 1250 = 3425

Therefore, Mr. Jensen's total income for selling 5 policies is $3425.

Conclusion

In this article, we explored the relationship between Mr. Jensen's salary and commission, and wrote an equation to represent this relationship in slope-intercept form. We analyzed the commission as a function of the number of policies sold, and then considered the total income as a function of the number of policies sold. Finally, we interpreted the equation and provided an example of how to use it to find Mr. Jensen's total income.

Key Takeaways

  • The equation represents the relationship between Mr. Jensen's total income and the number of policies he sells.
  • The slope of 250 represents the commission earned per policy sold.
  • The y-intercept of -2175 represents the base salary.
  • The equation can be used to find Mr. Jensen's total income for a given number of policies sold.

Further Reading

For more information on slope-intercept form and how to use it to represent relationships between variables, see the following resources:

Q: What is the base salary of Mr. Jensen?

A: The base salary of Mr. Jensen is $2,175.

Q: How much commission does Mr. Jensen earn per policy sold?

A: Mr. Jensen earns a commission of $250 per policy sold.

Q: What is the equation that represents the relationship between Mr. Jensen's total income and the number of policies he sells?

A: The equation is:

Total Income = 2175 + 250x

Q: What is the slope of the equation?

A: The slope of the equation is 250, which represents the commission earned per policy sold.

Q: What is the y-intercept of the equation?

A: The y-intercept of the equation is -2175, which represents the base salary.

Q: How can I use the equation to find Mr. Jensen's total income for a given number of policies sold?

A: To find Mr. Jensen's total income for a given number of policies sold, you can plug the number of policies sold into the equation. For example, if Mr. Jensen sells 5 policies, his total income would be:

Total Income = 2175 + 250(5) = 2175 + 1250 = 3425

Q: What if I want to find the number of policies Mr. Jensen needs to sell to earn a certain amount of money?

A: To find the number of policies Mr. Jensen needs to sell to earn a certain amount of money, you can rearrange the equation to solve for x. For example, if you want to find the number of policies Mr. Jensen needs to sell to earn $5,000, you can set up the equation as follows:

2175 + 250x = 5000

Subtracting 2175 from both sides gives:

250x = 2825

Dividing both sides by 250 gives:

x = 11.3

Therefore, Mr. Jensen would need to sell approximately 11.3 policies to earn $5,000.

Q: Can I use this equation to represent the relationship between Mr. Jensen's salary and commission for any given month?

A: Yes, you can use this equation to represent the relationship between Mr. Jensen's salary and commission for any given month. The equation is based on the assumption that Mr. Jensen earns a commission of $250 per policy sold, and that his base salary is $2,175. As long as these assumptions are true, the equation will accurately represent the relationship between Mr. Jensen's salary and commission.

Q: What if Mr. Jensen's commission rate changes?

A: If Mr. Jensen's commission rate changes, you will need to update the equation to reflect the new commission rate. For example, if Mr. Jensen's commission rate increases to $300 per policy sold, you can update the equation as follows:

Total Income = 2175 + 300x

Q: Can I use this equation to represent the relationship between Mr. Jensen's salary and commission for other salespeople?

A: No, this equation is specific to Mr. Jensen and his commission rate. If you want to represent the relationship between a different salesperson's salary and commission, you will need to create a new equation based on that salesperson's commission rate and base salary.

Conclusion

In this article, we answered frequently asked questions about Mr. Jensen's salary and commission. We covered topics such as the base salary, commission rate, equation, slope, y-intercept, and how to use the equation to find Mr. Jensen's total income for a given number of policies sold. We also discussed how to use the equation to represent the relationship between Mr. Jensen's salary and commission for any given month, and how to update the equation if Mr. Jensen's commission rate changes.