Certainly! Let's break down the equation and the components related to setting up the flowers for the party at LaMarge Inn.
Given:
[tex]\[ y = 10x + 20 \][/tex]
### Understanding the Equation
1. Number of flowers in welcome display:
- The equation [tex]\( y = 10x + 20 \)[/tex] represents the total number of flowers ([tex]\( y \)[/tex]).
- The welcome display is indicated by the constant term, which is 20. This is because it does not depend on the number of centerpieces ([tex]\( x \)[/tex]).
2. Number of flowers per centerpiece:
- The coefficient of [tex]\( x \)[/tex] in the equation [tex]\( y = 10x + 20 \)[/tex] is 10. This represents the number of flowers in each centerpiece.
3. Number of centerpieces ([tex]\( x \)[/tex]):
- Here, [tex]\( x \)[/tex] is the variable representing the number of centerpieces.
### Breakdown of the Given Values
- Y-Intercept:
- The y-intercept of the equation [tex]\( y = 10x + 20 \)[/tex] is 20. This is the number of flowers in the welcome display, as it is the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex].
- Slope:
- The slope of the equation is 10, which represents the number of flowers in each centerpiece. For every 1 centerpiece added, 10 additional flowers are included in the total count.
### Key Values
- Number of flowers in welcome display:
- This is 20, derived from the y-intercept.
- Number of flowers per centerpiece:
- This is 10, derived from the slope.
### Overall Equation
To find the total number of flowers ([tex]\( y \)[/tex]) based on the number of centerpieces ([tex]\( x \)[/tex]):
[tex]\[ y = 10x + 20 \][/tex]
- [tex]\[ y \][/tex]: Total number of flowers.
- [tex]\[ x \][/tex]: Number of centerpieces.
- [tex]\[ 10x \][/tex]: Number of flowers contributed by the centerpieces.
- [tex]\[ + 20 \][/tex]: Number of flowers in the welcome display.
So, revisiting the items from the input and output section:
### Input
- Number of centerpieces ([tex]\( x \)[/tex])
### Output
- Number of flowers per centerpiece: 10
- Number of flowers in the welcome display: 20
- Total number of flowers: [tex]\( y = 10x + 20 \)[/tex], where [tex]\( x \)[/tex] is the number of centerpieces.
To summarize, the setup of the party decorations can be completely described by knowing there are 20 flowers in the welcome display and 10 flowers in each centerpiece, represented by the equation [tex]\( y = 10x + 20 \)[/tex].
