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?
Unfortunately, since the table and graph are not provided, we cannot determine the equation that represents the proportional relationship between the earnings and hours worked for Employee 1 and Employee 2.
To find the equation that represents the proportional relationship between the earnings and hours worked for Employee 1, we can look at the pattern in the table. The earnings are increasing by 10 each time the hours worked increase by 1. So, we can write the equation as:
Earnings = 10 * hours worked
For Employee 2, we can observe the pattern in the graph. The earnings are increasing at a faster rate than the hours worked. The graph appears to be a linear relationship, so we can use the equation of a line, y = mx + b, to represent it. From the data provided, we can see that when the hours worked are 1, the earnings are 15, which gives us a point (1, 15). Using the point-slope form of a linear equation, we have:
y - y1 = m(x - x1)
y - 15 = m(x - 1)
y - 15 = mx - m
y = mx + (15 - m)
To find the slope, m, we can use another point on the graph, for example, (2, 45). Plugging in the values in the equation, we get:
45 = 2m + (15 - m)
30 = m
Thus, the equation that represents the proportional relationship between the earnings and hours worked for Employee 2 is:
Earnings = 30 * hours worked + (15 - 30)
Earnings = 30 * hours worked - 15
The equation for Employee 1 is
The equation for Employee 2 is
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employee 1: 1 10 2 20 3 30
employee 2: 1 15 2 45 3 70
For Employee 1, the equation representing the proportional relationship between earnings and hours worked is:
Earnings = 10 * hours worked
For Employee 2, the equation representing the proportional relationship between earnings and hours worked is:
Earnings = 15 * hours worked - 15
I apologize for the mistake. Let's go through the given data again:
Employee 1:
- Earnings: 10, 20, 30
- Hours Worked: 1, 2, 3
For Employee 1, we can see that the earnings are increasing by 10 as the hours worked increases by 1. Therefore, the equation representing the proportional relationship is:
Earnings = 10 * Hours Worked
Now let's consider Employee 2:
- Earnings: 15, 45, 70
- Hours Worked: 1, 2, 3
To find the equation representing the proportional relationship for Employee 2, we need to determine the ratio of earnings to hours worked. Taking any two points, such as (1, 15) and (2, 45), we can calculate the slope:
Slope = (Change in Y) / (Change in X)
= (45 - 15) / (2 - 1)
= 30 / 1
= 30
This tells us that the earnings increase by 30 for every 1 unit increase in hours worked. To find the equation, we can use the point-slope form and plug in the values of one of the points. Let's use (1,15):
Earnings - 15 = 30 * (Hours Worked - 1)
Simplifying the equation:
Earnings = 30 * Hours Worked - 15
Therefore, the equation representing the proportional relationship for Employee 2 is:
Earnings = 30 * Hours Worked - 15