Subjects algebra

Overtime Pay Ca3578

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1. **State the problem:** Mai earns a fixed wage plus extra money for every hour of overtime she works. The graph shows her total pay (in dollars) versus the amount of overtime (in hours). We need to find: (a) Mai's total pay with 0 hours of overtime. (b) The relationship between overtime and total pay, and the rate of change. 2. **Analyze the graph:** From the graph description, the line starts at about $125$ dollars when overtime is $0$ hours. 3. **Answer (a):** Mai's total pay with $0$ hours of overtime is the fixed wage, which is the y-intercept of the graph. So, total pay at $0$ hours overtime is: $$y = 125$$ 4. **Answer (b):** The graph shows a positive linear relationship, meaning as overtime increases, total pay increases. 5. **Find the rate of increase:** From the graph, at $0$ hours overtime, pay is $125$ dollars. At $3$ hours overtime, pay is near $250$ dollars. The rate of increase (slope) is: $$\text{slope} = \frac{250 - 125}{3 - 0} = \frac{125}{3} = 41.67$$ So, the total pay increases by approximately $41.67$ dollars per hour of overtime. 6. **Summary:** - Mai's total pay with $0$ hours overtime is $125$ dollars. - As overtime increases, total pay increases. - The rate of increase is about $41.67$ dollars per hour. Final answers: (a) $125$ (b) As the amount of overtime increases, the total pay increases. Rate: $41.67$ per hour