Sure! Let's explore the given algebraic expressions in detail:
1. Expression: [tex]\( n-9 \)[/tex]
- This is a linear expression where 9 is subtracted from the variable [tex]\( n \)[/tex].
- In terms of its graphical representation, this would be a line shifted downward by 9 units from the standard linear graph of [tex]\( y = n \)[/tex].
2. Expression: [tex]\( n+9 \)[/tex]
- This is another linear expression, but in this case, we are adding 9 to the variable [tex]\( n \)[/tex].
- Graphically, this line is shifted upward by 9 units from the baseline linear graph of [tex]\( y = n \)[/tex].
3. Expression: [tex]\( 9n \)[/tex]
- Here, [tex]\( n \)[/tex] is multiplied by 9. This is a linear expression where the slope is 9.
- Graphically, this is a much steeper line compared to [tex]\( y = n \)[/tex] due to the multiplication factor.
4. Expression: [tex]\( \frac{n}{9} \)[/tex]
- This expression divides [tex]\( n \)[/tex] by 9.
- Graphically, this line is less steep, having a slope of [tex]\( \frac{1}{9} \)[/tex], compared to the standard linear graph of [tex]\( y = n \)[/tex].
To summarize, the algebraic expressions provided are:
- [tex]\( n-9 \)[/tex]: The variable [tex]\( n \)[/tex] with a subtraction of 9.
- [tex]\( n+9 \)[/tex]: The variable [tex]\( n \)[/tex] with an addition of 9.
- [tex]\( 9n \)[/tex]: The variable [tex]\( n \)[/tex] multiplied by 9.
- [tex]\( \frac{n}{9} \)[/tex]: The variable [tex]\( n \)[/tex] divided by 9.
Each of these expressions transforms the variable [tex]\( n \)[/tex] in a different way and subsequently would have different graphical representations.
