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Which function has the same graph as [tex]x + y = 11[/tex]?

A. [tex]f(x) = -y + 11[/tex]
B. [tex]f(x) = -x + 11[/tex]
C. [tex]f(x) = x - 11[/tex]
D. [tex]f(x) = y - 11[/tex]

Sagot :

GinnyAnswer
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].
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