Math Problem Statement

answer

The following graph represents the relationship between hours worked and pay for an employee. This employee earns a base salary and an additional amount that is dependent on the number of hours they work. Determine their base salary and their hour rate.

Solution

To determine the base salary and hourly rate, we use the two given points on the graph:

  • (0,400)(0, 400): This is the point where x=0x = 0 (no hours worked), so the corresponding yy-value 400400 represents the base salary.
  • (10,615)(10, 615): This point tells us that after working 10 hours, the total pay is 615615.

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: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} Here:

  • (x1,y1)=(0,400)(x_1, y_1) = (0, 400)
  • (x2,y2)=(10,615)(x_2, y_2) = (10, 615)

Substitute the values: m=615400100=21510=21.5m = \frac{615 - 400}{10 - 0} = \frac{215}{10} = 21.5 Thus, the hourly rate is 21.521.5 (dollars per hour).


Step 2: Base salary

The base salary is the yy-intercept, which is the value of yy when x=0x = 0. From the point (0,400)(0, 400), we know: Base salary=400\text{Base salary} = 400


Final Answer:

  1. Base salary = $400
  2. Hourly rate = $21.50 per hour

Let me know if you'd like further details or help with related problems!


Related Questions:

  1. How do you calculate the equation of the line using the slope and intercept?
  2. If the employee works 15 hours, what will their total pay be?
  3. How can you determine the slope if the points are not given explicitly on a graph?
  4. What does the slope of the line represent in real-life contexts like this one?
  5. How would the graph change if the hourly rate increases to 2525 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.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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