Let's address each part of your question step-by-step.
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What is the y-intercept?
Answer: The y-intercept is 38,000.
Explanation: In the equation \(y = 0.28x + 38,000\), the y-intercept (the value of y when x = 0) is the constant term, which is 38,000. -
What does the y-intercept mean in context?
Answer: The y-intercept represents Adam's base salary.
Explanation: When Adam has no sales (x = 0), his total salary (y) is 38,000, which is his base salary regardless of his sales performance. -
What is the slope?
Answer: The slope is 0.28.
Explanation: In the equation \(y = 0.28x + 38,000\), the slope (0.28) quantifies the rate of change in Adam's salary with respect to his sales. -
What does the slope mean in context?
Answer: The slope means that for every dollar increase in total sales, Adam’s salary increases by $0.28.
Explanation: This means that Adam earns 28 cents for every dollar he sells in commission on top of his base salary. -
If Adam made $45,000 total annual salary, how much was his total sales?
To find x (total sales), set y = 45,000 in the equation and solve for x:
\[ 45,000 = 0.28x + 38,000 \] \[ 45,000 - 38,000 = 0.28x \] \[ 7,000 = 0.28x \] \[ x = \frac{7,000}{0.28} \approx 25,000 \]
Answer: Adam's total sales were approximately $25,000.
So, summarizing the answers:
- y-intercept: 38,000
- Meaning of the y-intercept: Adam's base salary
- Slope: 0.28
- Meaning of the slope: The increase in salary per total dollar sales
- Total sales if salary is $45,000: Approximately $25,000