Employee 1
Earnings per Hour
Hours Earnings
1 10
2 20
3 30
A line graph is titled as Employee 2, Earnings per Hour. The x-axis is labeled Hours ranging from 0 to 6 in increments of 1. The y-axis is labeled Earnings in dollars, ranging from 0 to 80 in increments of 5. A solid line joins four plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 15 right parenthesis, left parenthesis 3 comma 45 right parenthesis, and left parenthesis 5 comma 75 right parenthesis.
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 can be determined by finding the ratio between the earnings and the hours worked. Since the earnings increase by 10 for each hour worked, the equation can be written as:
Earnings = 10 * Hours
The equation for Employee 2 can be determined by finding the slope of the line connecting the plotted points. The slope is calculated by finding the difference in y-values divided by the difference in x-values.
slope = (y2 - y1) / (x2 - x1)
= (15 - 0) / (1 - 0)
= 15
Using the slope-intercept form of a line (y = mx + b), we can substitute the slope and one of the points (1, 15) to solve for the y-intercept (b):
15 = 15 * 1 + b
b = 0
Therefore, the equation for Employee 2 is:
Earnings = 15 * Hours
incorrect
I apologize for the incorrect response. To find the equation for Employee 1, we can observe that the earnings increase by 10 for each hour worked. This suggests that there is a constant rate of change or slope of 10. Additionally, we can see that the initial earnings when working 0 hours is 0.
Therefore, the equation for Employee 1 is:
Earnings = 10 * Hours
Now let's find the equation for Employee 2 using the given points (0, 0), (1, 15), (3, 45), and (5, 75).
The slope of the line connecting these points can be found using the slope formula:
slope = (y2 - y1) / (x2 - x1)
= (15 - 0) / (1 - 0)
= 15/1
= 15
To find the equation, we can use the slope-intercept form of a line (y = mx + b), where m is the slope and b is the y-intercept. Plugging in the slope and one of the points (0,0) into the equation:
0 = 15 * 0 + b
b = 0
Therefore, the equation for Employee 2 is:
Earnings = 15 * Hours
Store B
Cost of Gasoline per Gallon
Gallons ($) Cost
5 18.75
10 37.50
15 56.25
The proportional relationships between the cost and the number of gallons of gasoline for Store A and Store B are displayed in the graph and table. Which store has the better buy for a gallon of gasoline? Enter 1 for Store A. Enter 2 for Store B.
(1 point)
has the better buy for a gallon of gasoline.
To determine which store has the better buy for a gallon of gasoline, we can compare the cost per gallon in each store.
For Store A, the cost per gallon is $3.50.
For Store B, the cost per gallon can be found by dividing the cost by the number of gallons. The cost per gallon for Store B is as follows:
For 5 gallons: $18.75 / 5 = $3.75
For 10 gallons: $37.50 / 10 = $3.75
For 15 gallons: $56.25 / 15 = $3.75
The cost per gallon is consistent at $3.75 for Store B.
Comparing the cost per gallon, we see that Store A has a better buy for a gallon of gasoline since it is priced at $3.50, which is lower than Store B's price of $3.75.
Therefore, Store A (1) has the better buy for a gallon of gasoline.
The equation for Employee 1 can be derived by observing that the earnings per hour increase linearly by a rate of $10 per hour. Therefore, the equation representing this proportional relationship can be written as:
Earnings = 10 * Hours
The equation for Employee 2 can be derived from the plotted points on the graph. Since the earnings increase by $15 for every 1-hour increase in working hours, the equation can be written as:
Earnings = 15 * Hours
So, the equations representing the proportional relationships between the earnings and hours worked for Employee 1 and Employee 2 are:
For Employee 1: Earnings = 10 * Hours
For Employee 2: Earnings = 15 * Hours
To find the equation for the proportional relationship between earnings and hours worked for Employee 1, we can observe the table:
Hours: 1, 2, 3
Earnings: 10, 20, 30
We can see that the earnings for Employee 1 are increasing by 10 for each additional hour worked. Therefore, the equation for Employee 1 is:
Earnings = 10 * Hours
Now let's find the equation for Employee 2 using the graph:
The graph shows the following points: (0, 0), (1, 15), (3, 45), (5, 75)
From the coordinates, we can see that the earnings for Employee 2 are increasing by 15 for each additional hour worked. Therefore, the equation for Employee 2 is:
Earnings = 15 * Hours