Math Problem Statement
answer
Solution
To determine the base salary and hourly rate, we use the two given points on the graph:
- : This is the point where (no hours worked), so the corresponding -value represents the base salary.
- : This point tells us that after working 10 hours, the total pay is .
Step 1: Hourly rate (slope of the line)
The hourly rate is the slope of the line, which can be calculated using the slope formula: Here:
Substitute the values: Thus, the hourly rate is (dollars per hour).
Step 2: Base salary
The base salary is the -intercept, which is the value of when . From the point , we know:
Final Answer:
- Base salary = $400
- Hourly rate = $21.50 per hour
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Related Questions:
- How do you calculate the equation of the line using the slope and intercept?
- If the employee works 15 hours, what will their total pay be?
- How can you determine the slope if the points are not given explicitly on a graph?
- What does the slope of the line represent in real-life contexts like this one?
- How would the graph change if the hourly rate increases to dollars per hour?
Tip: The slope of a line shows the rate of change, which is useful for understanding relationships like pay per hour in this problem.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Slope
Y-intercept
Rate of Change
Formulas
Slope Formula: m = (y2 - y1) / (x2 - x1)
Linear Equation: y = mx + b
Theorems
Concept of Slope
Linear Relationship
Suitable Grade Level
Grades 8-10
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