Question

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.(5 points)
Y intercept and its meaning
Slope and it’s meaning
If he made 45,000 annually, what would be his total sales

Answer 1

Let's analyze the equation \( y = 0.28x + 38,000 \) step by step.

### Y-Intercept
The y-intercept is the value of \( y \) when \( x = 0 \). In this case, the y-intercept is \( 38,000 \).

**Meaning**: The y-intercept represents Adam's base salary, which he receives irrespective of his sales. It indicates that even if he does not make any sales (\( x = 0 \)), he will still earn $38,000 annually.

### Slope
The slope is the coefficient of \( x \) in the equation, which is \( 0.28 \).

**Meaning**: The slope represents the commission rate on Adam's total sales. Specifically, for every dollar of sales Adam makes, he earns an additional $0.28 in commission. It reflects how much his total annual salary increases with each additional dollar of sales.

### Calculating Total Sales if Annual Salary is $45,000
To find out Adam's total sales when his annual salary \( y \) is $45,000, we can substitute \( y \) with $45,000 in the equation and solve for \( x \):

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

Now, subtract $38,000 from both sides:

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

\[
7,000 = 0.28x
\]

Next, divide both sides by 0.28 to isolate \( x \):

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

Calculating this gives:

\[
x = 25,000
\]

### Conclusion
If Adam made $45,000 annually, his total sales would be $25,000.