To find the equation that represents Mr. Jensen's total monthly paycheck based on the number of policies he sells, we need to consider two parts of his income:
1. Base Salary: This is the fixed amount of money Mr. Jensen receives each month, regardless of how many policies he sells. Given that his base salary is \[tex]$2,175, this will be the constant part of the equation.
2. Commission: This is the additional amount Mr. Jensen earns for each policy he sells. He earns \$[/tex]250 for each policy. Therefore, the commission part is calculated by multiplying the number of policies sold [tex]\( x \)[/tex] by 250.
Combining these two parts, the total monthly paycheck [tex]\( y \)[/tex] can be represented as the sum of the base salary and the commission earned from selling [tex]\( x \)[/tex] policies.
### Slope-Intercept Form of the Equation
The slope-intercept form of a linear equation is given by:
[tex]\[ y = mx + b \][/tex]
where:
- [tex]\( y \)[/tex] is the total income,
- [tex]\( m \)[/tex] is the slope (which represents the rate of change, in this case, the commission per policy),
- [tex]\( x \)[/tex] is the number of policies sold,
- [tex]\( b \)[/tex] is the y-intercept (which represents the base salary).
Given:
- The base salary [tex]\( b \)[/tex] is 2175,
- The commission per policy [tex]\( m \)[/tex] is 250,
We substitute these values into the slope-intercept form:
[tex]\[ y = 250x + 2175 \][/tex]
This equation accurately represents the total monthly paycheck [tex]\( y \)[/tex] of Mr. Jensen based on the number of policies [tex]\( x \)[/tex] he sells.
