To find the slope of a line from Ava's expression \(5 - 14 - 2\), we first simplify the expression:
- Calculate \( 14 + 2 = 16\).
- Then, \( 5 - 16 = -11\).
So, the slope of the line is \(-11\).
Now we need to determine which table represents a line with a slope of \(-11\). The slope \(m\) of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
To check each option, we will calculate the slopes between the points in each table.
Option 1:
| x | y | |---|---| | 5 | 4 | | 1 | 2 |
Calculating the slope: \[ m = \frac{2 - 4}{1 - 5} = \frac{-2}{-4} = \frac{1}{2} \] Not -11
Option 2:
| x | y | |---|---| | 2 | 1 | | 4 | 5 |
Calculating the slope: \[ m = \frac{5 - 1}{4 - 2} = \frac{4}{2} = 2 \] Not -11
Option 3:
| x | y | |---|---| | 2 | 5 | | 4 | 1 |
Calculating the slope: \[ m = \frac{1 - 5}{4 - 2} = \frac{-4}{2} = -2 \] Not -11
Option 4:
| x | y | |---|---| | 4 | -5 | | 2 | -1 |
Calculating the slope: \[ m = \frac{-1 - (-5)}{2 - 4} = \frac{4}{-2} = -2 \] Not -11
None of the provided tables show a slope of \(-11\). Each table we calculated has different slopes which do not match what we set out to find.
There might be an error in Ava's calculation or the options given. If specific line coordinates were intended to yield that slope, please check again for any additional information or corrections in options.