Let's take a detailed look at the given equation and options to determine which function has the same graph as [tex]\( x + y = 11 \)[/tex].
We'll start by manipulating the equation [tex]\( x + y = 11 \)[/tex] to find an equivalent function in the form [tex]\( y = f(x) \)[/tex].
1. The original equation is:
[tex]\[
x + y = 11
\][/tex]
2. To express [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex], we need to isolate [tex]\( y \)[/tex]. Subtract [tex]\( x \)[/tex] from both sides of the equation:
[tex]\[
y = 11 - x
\][/tex]
3. Now, we have the function:
[tex]\[
y = 11 - x
\][/tex]
This function [tex]\( y = 11 - x \)[/tex] can be written as [tex]\( f(x) = 11 - x \)[/tex]. Another equivalent way to express this function is [tex]\( f(x) = -x + 11 \)[/tex].
Now let's examine the options given in the question to determine which matches [tex]\( f(x) = -x + 11 \)[/tex]:
A. [tex]\( f(x) = -y + 11 \)[/tex]
This does not match our derived function.
B. [tex]\( f(x) = -x + 11 \)[/tex]
This matches our derived function [tex]\( f(x) = 11 - x \)[/tex].
C. [tex]\( f(x) = x - 11 \)[/tex]
This does not match our derived function.
D. [tex]\( f(x) = y - 11 \)[/tex]
This does not match our derived function.
Thus, the function that has the same graph as [tex]\( x + y = 11 \)[/tex] is:
B. [tex]\( f(x) = -x + 11 \)[/tex]
