To find the y-value when \( x = 13 \) for the function \( y = \sqrt{12x + 3} - 9 \), we can follow these steps:
- Substitute \( x = 13 \) into the function:
\[ y = \sqrt{12(13) + 3} - 9 \]
- Calculate \( 12(13) + 3 \):
\[ 12(13) = 156 \quad \text{so} \quad 156 + 3 = 159 \]
- Now take the square root:
\[ y = \sqrt{159} - 9 \]
- Calculate \( \sqrt{159} \) (we can either estimate its value or recognize it's between integer values):
The square root of 159 is approximately 12.57, because:
\[ 12^2 = 144 \quad \text{and} \quad 13^2 = 169 \]
- Now, substitute back to find \( y \):
\[ y \approx 12.57 - 9 = 3.57 \]
Since the provided answers are integers, we evaluate \( \sqrt{159} - 9 \):
\[ \sqrt{159} \text{ is approximately } 12.57 \Rightarrow 3.57 \]
None of the options (−1, −5, 2, −7) match this approximate value. Checking for possible integer outputs:
- Since \( \sqrt{159} \) is greater than \( 9 \) when calculating for \( y \), we conclude the result is above zero.
Therefore, the right choice from the provided answers is:
2.