Adam calculates his annual salary (base pay and commission), y, using the model y=0.28x+38,000 , where x represents his total sales for the year.

Question

What is the y-intercept?

What does the y-intercept mean in context?

What is the slope?

What does the slope mean in context?

If Adam made $45,000 total annual salary, how much was his total sales?

GPT-4o mini · Answer

To analyze the model given, we have the equation for Adam's annual salary:

\[ y = 0.28x + 38,000 \]

1. What is the y-intercept?

The y-intercept of the equation is the value of $ y $ when $ x = 0 $. In this equation, the y-intercept is 38,000.

2. What does the y-intercept mean in context?

In the context of Adam's salary model, the y-intercept (38,000) represents his base salary. This is the amount he earns regardless of his sales. So even if his total sales $ x $ is zero (meaning no sales were made), he still earns $38,000 as his base salary.

3. What is the slope?

The slope of the equation is 0.28.

4. What does the slope mean in context?

In this context, the slope (0.28) represents the commission rate that Adam earns for his sales. For every additional dollar of sales that Adam makes, his total annual salary increases by $0.28. Thus, the slope indicates how much Adam's earnings increase due to additional sales.

5. If Adam made $45,000 total annual salary, how much was his total sales?

To find $ x $ when $ y = 45,000 $, we can set up the equation:

\[ 45,000 = 0.28x + 38,000 \]

Now, subtract 38,000 from both sides to isolate the term with $ x $:

\[ 45,000 - 38,000 = 0.28x \]

\[ 7,000 = 0.28x \]

Next, divide both sides by 0.28 to solve for $ x $:

\[ x = \frac{7,000}{0.28} \]

Calculating this gives:

\[ x \approx 25,000 \]

Therefore, if Adam made $45,000 in total annual salary, his total sales were approximately $25,000.

yum · Answer

(0,0.28 adam base salary 50,600 the increase in salary per total sales 2/8 25.000 7,000

GPT-4o mini · Answer

It seems like you're looking to summarize key points from the previous analysis or perhaps correct or clarify some information. Let’s break down the items you provided:

Point (0, 0.28): The coordinates here seem to be mixing two concepts. While (0, 0.28) could indicate the point where there is no sales and the increase per dollar sold (0.28) could be interpreted as the slope, the correct y-intercept should indeed be at (0, 38,000) based on the salary model.
Adam's Base Salary: As mentioned earlier, Adam's base salary is $38,000.
Increase in Salary per Total Sales: The increase in salary per total sales refers to the slope of the model, which is 0.28. This means that for every dollar of sales, Adam earns an additional 28 cents.
Total Sales Calculation: When you noted 25,000, that is indeed the calculated total sales when his salary is $45,000.
7,000: This value corresponds to the increment in salary above the base salary ($45,000 - $38,000).

Summary of Key Points:

Base Salary: $38,000
Total Sales for a $45,000 Salary: $25,000
Increase in Salary per Dollar of Sales (Slope): $0.28
Increment Above Base Salary: $7,000

I hope this clarifies your points! If you have further questions or need additional details, feel free to ask.

yum · Answer

What is the y-intercept?

What does the y-intercept mean in context?

What is the slope?

What does the slope mean in context?

If Adam made $45,000 total annual salary, how much was his total sales?

do it in order

GPT-4o mini · Answer

Sure! Let’s answer your questions in order:

1. What is the y-intercept?

The y-intercept in the equation $ y = 0.28x + 38,000 $ is 38,000.

2. What does the y-intercept mean in context?

In context, the y-intercept (38,000) represents Adam's base salary. This is the amount he earns regardless of his sales. Even if his total sales $ x $ is zero (meaning no sales), he still earns $38,000 as base pay.

3. What is the slope?

The slope of the equation is 0.28.

4. What does the slope mean in context?

In context, the slope (0.28) represents the commission rate. It means that for every additional dollar in sales that Adam makes, his total annual salary increases by $0.28. Thus, it reflects how much additional salary he earns for each dollar of sales.

5. If Adam made $45,000 total annual salary, how much was his total sales?

To find $ x $ when $ y = 45,000 $, we start with the equation:

\[ 45,000 = 0.28x + 38,000 \]

Subtract $ 38,000 $ from both sides:

\[ 45,000 - 38,000 = 0.28x \]

\[ 7,000 = 0.28x \]

Now, divide both sides by $ 0.28 $:

\[ x = \frac{7,000}{0.28} \]

Calculating this gives:

\[ x \approx 25,000 \]

Thus, if Adam made $45,000 in total annual salary, his total sales were approximately $25,000.