To solve this problem step-by-step, let's break down the information given about Eric and Bailey's earnings.
1. Eric's Earnings:
- The equation [tex]\( y = 10x + 50 \)[/tex] represents Eric's weekly earnings.
- In this equation, [tex]\( x \)[/tex] represents the number of items sold by Eric.
- The coefficient [tex]\( 10 \)[/tex] is the commission rate per item sold.
- The constant term [tex]\( 50 \)[/tex] is Eric's weekly salary (the fixed amount he earns regardless of sales).
2. Bailey's Earnings:
- Bailey earns a greater weekly salary than Eric, but the same commission rate.
- This means the commission rate for Bailey will also be [tex]\( 10 \)[/tex] (the same as Eric's).
3. Bailey's Weekly Salary:
- Since Bailey's salary is greater than Eric's, we denote her weekly salary as an increased amount over Eric's [tex]$50.
- Let's assume Bailey’s salary is $[/tex]20 more than Eric's weekly salary.
4. Constructing Bailey's Earnings Equation:
- Eric’s weekly salary is \[tex]$50.
- Bailey’s weekly salary, which is \$[/tex]20 more than Eric’s, will be [tex]\( 50 + 20 = 70 \)[/tex].
5. Bailey's Earnings Equation:
- Combining Bailey’s weekly salary with the same commission rate, Bailey’s earnings equation can be written as:
[tex]\[
y = 10x + 70
\][/tex]
Here, [tex]\( y \)[/tex] represents Bailey’s weekly earnings, and [tex]\( x \)[/tex] represents the number of items sold.
6. Graphing Bailey's Earnings Equation:
- The graph of Bailey’s weekly earnings will be a straight line since it’s a linear equation.
- This line will have the same slope (commission rate) as Eric's line, which is [tex]\( 10 \)[/tex].
- The y-intercept (weekly salary, when [tex]\( x = 0 \)[/tex]) for Bailey’s line will be [tex]\( 70 \)[/tex], which is higher than Eric's y-intercept of [tex]\( 50 \)[/tex].
Therefore, the graph representing Bailey’s earnings would be a line parallel to Eric's earnings line but shifted upwards by 20 units.
Given this detailed process, the amount of money that Bailey earns weekly, based on the number of items sold [tex]\( x \)[/tex], is represented by the equation:
[tex]\[
y = 10x + 70
\][/tex]
This concludes that the graph showing Bailey's earnings will have the same slope as Eric's but will start at [tex]\( 70 \)[/tex] on the y-axis instead of [tex]\( 50 \)[/tex].
