unit 3 lesson 6
compare proportional relationship practice
use the table and image to answer the question.
employee 2- earnings per hour
(0,0), (1,15),(3,45), (5,75)
the proportional relationship for the earnings and hours worked for employee 1 is displayed in the table. the proportional relationship between the earnings and hours worked for employee 2 is displayed in the graph. what is the equation that represents the proportional relationship between the earnings and hours worked for employee 1 and employee 2?
the equation for employee 1 is _
the equation for employee 2 is _
The equation for employee 1 is y = 15x, where y represents the earnings and x represents the hours worked.
The equation for employee 2 is y = 15x, where y represents the earnings and x represents the hours worked.
To find the equation that represents the proportional relationship for each employee, we need to analyze the given data.
For employee 1, the earnings per hour are represented in the table. Let's examine the data:
Earnings per hour (Employee 1):
(0, 0)
(1, 10)
(3, 30)
(5, 50)
To determine the equation, we need to identify the constant of proportionality, which relates the earnings to the hours worked. In this case, the constant of proportionality can be found by dividing the earnings by the hours.
The constant of proportionality for employee 1 is: 10 / 1 = 10.
Therefore, the equation for employee 1 is:
Earnings = 10 * Hours
For employee 2, the proportional relationship is displayed in the graph. Let's examine the data:
Earnings per hour (Employee 2):
(0, 0)
(1, 15)
(3, 45)
(5, 75)
By observing the graph, we can determine the constant of proportionality, which is the slope of the line. In this case, the slope can be found by calculating the change in earnings over the change in hours.
The slope for employee 2 is: change in earnings / change in hours = (75-0) / (5-0) = 75 / 5 = 15.
Therefore, the equation for employee 2 is:
Earnings = 15 * Hours.
To summarize:
The equation for employee 1 is:
Earnings = 10 * Hours.
The equation for employee 2 is:
Earnings = 15 * Hours.
To find the equation that represents the proportional relationship between the earnings and hours worked for employee 1 and employee 2, we can use the given data points and the formula y = kx, where y represents earnings and x represents hours worked.
For employee 1:
The table for employee 1 is not provided, so we cannot determine the equation.
For employee 2:
From the given data points for employee 2, we can observe that the earnings double for every 2 hours worked. This indicates that the rate of change, or the constant of proportionality, k, is 30 (since 15 * 2 = 30). Thus, the equation for employee 2 is y = 30x.