To determine if the table and the equation represent the same function, we need to compare the [tex]\(y\)[/tex]-values calculated using the equation [tex]\( y = 390 + 11x \)[/tex] with the [tex]\(y\)[/tex]-values provided in the table for the same [tex]\(x\)[/tex]-values.
1. For [tex]\( x = -50 \)[/tex]:
[tex]\[
y = 390 + 11(-50) = 390 - 550 = -160
\][/tex]
The table value is [tex]\(-180\)[/tex]. These values do not match.
2. For [tex]\( x = -45 \)[/tex]:
[tex]\[
y = 390 + 11(-45) = 390 - 495 = -105
\][/tex]
The table value is [tex]\(-110\)[/tex]. These values do not match.
3. For [tex]\( x = -40 \)[/tex]:
[tex]\[
y = 390 + 11(-40) = 390 - 440 = -50
\][/tex]
The table value is [tex]\(-40\)[/tex]. These values do not match.
4. For [tex]\( x = -35 \)[/tex]:
[tex]\[
y = 390 + 11(-35) = 390 - 385 = 5
\][/tex]
The table value is [tex]\(30\)[/tex]. These values do not match.
5. For [tex]\( x = -30 \)[/tex]:
[tex]\[
y = 390 + 11(-30) = 390 - 330 = 60
\][/tex]
The table value is [tex]\(100\)[/tex]. These values do not match.
Since none of the calculated [tex]\(y\)[/tex]-values match the [tex]\(y\)[/tex]-values provided in the table for the given [tex]\(x\)[/tex]-values, we conclude that the table and the equation do not represent the same function.
Correct answer: No
