To determine which function has the same graph as the equation [tex]\( x + y = 11 \)[/tex], we can rewrite the given equation in a more familiar form, such as the slope-intercept form of a line [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept. Here are the steps to rewrite the equation and identify the correct function:
1. Starting with the given equation:
[tex]\[
x + y = 11
\][/tex]
2. Isolate [tex]\( y \)[/tex] to rewrite the equation in slope-intercept form:
[tex]\[
y = -x + 11
\][/tex]
Now, we compare the rewritten equation [tex]\( y = -x + 11 \)[/tex] with the given options to determine which one matches this form:
- Option A: [tex]\( f(x) = -y + 11 \)[/tex]
[tex]\[
\text{This is not equivalent to } y = -x + 11.
\][/tex]
- Option B: [tex]\( f(x) = -x + 11 \)[/tex]
[tex]\[
\text{This is exactly the same as } y = -x + 11.
\][/tex]
- Option C: [tex]\( f(x) = x - 11 \)[/tex]
[tex]\[
\text{This is not equivalent to } y = -x + 11.
\][/tex]
- Option D: [tex]\( f(x) = y - 11 \)[/tex]
[tex]\[
\text{This is not equivalent to } y = -x + 11.
\][/tex]
Thus, the correct function that has the same graph as the equation [tex]\( x + y = 11 \)[/tex] is:
Option B: [tex]\( f(x) = -x + 11 \)[/tex].
