Question 1166455
This is a comparison problem based on the properties of linear equations, specifically the slope and the y-intercept.

The correct graph representing Bailey's weekly earnings will be a line that is **parallel to Eric's graph** but **shifted vertically higher** on the coordinate plane .

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## 📈 Analysis of the Earnings Equations

Both Eric's and Bailey's earnings can be modeled by a linear equation in the slope-intercept form: $y = mx + b$.

* $y$: Total weekly earnings.
* $x$: Number of items sold.
* $m$: **Commission rate** (slope).
* $b$: **Weekly salary** (y-intercept).

### 1. Eric's Earnings

Eric's equation is: $y = 10x + 50$
* **Slope ($m_{Eric}$):** $10$. This is his commission rate per item sold.
* **Y-intercept ($b_{Eric}$):** $50$. This is his weekly salary.

### 2. Bailey's Earnings

The prompt gives two conditions for Bailey's equation:

* **Same commission rate:** This means Bailey's slope ($m_{Bailey}$) must be the same as Eric's slope ($m_{Eric}$).
    $$m_{Bailey} = 10$$
    * In graphical terms, the two lines must be **parallel**.

* **Greater weekly salary:** This means Bailey's y-intercept ($b_{Bailey}$) must be greater than Eric's y-intercept ($b_{Eric} = 50$).
    $$b_{Bailey} > 50$$
    * In graphical terms, Bailey's line must cross the y-axis at a **higher point** than Eric's line.

## 🖼️ Conclusion for Bailey's Graph

The graph that represents Bailey's earnings must satisfy these two conditions:

1.  **It must be a line with the same steepness (slope of 10) as Eric's line.**
2.  **It must be a line that starts at a higher y-intercept (a point above 50 on the y-axis).**

Therefore, the graph that represents Bailey's earnings is a **parallel line that lies entirely above Eric's line**.