To determine which function has the same graph as the equation [tex]\( x + y = 11 \)[/tex], we will rewrite the equation in a more familiar form.
1. Start with the given equation:
[tex]\[ x + y = 11 \][/tex]
2. Solve for [tex]\( y \)[/tex] to express the equation in the form [tex]\( y = \text{something} \)[/tex]:
[tex]\[ y = -x + 11 \][/tex]
3. Now, let's compare this with the given options:
- Option A: [tex]\( f(x) = -y + 11 \)[/tex]
- Option B: [tex]\( 1(x) = -x + 11 \)[/tex]
- Option C: [tex]\( f(x) = x - 11 \)[/tex]
- Option D: [tex]\( f(x) = y - 11 \)[/tex]
4. Looking at these options, the function that matches the form [tex]\( y = -x + 11 \)[/tex] is:
- Option B: [tex]\( 1(x) = -x + 11 \)[/tex]
Therefore, the function that has the same graph as [tex]\( x + y = 11 \)[/tex] is:
Option B: [tex]\( 1(x) = -x + 11 \)[/tex].
