To determine the slope from Ava's expression \( 5 - \frac{1}{4} - 2 \), we first simplify it.
- Start with \( 5 - 2 = 3 \).
- Then, subtract \( \frac{1}{4} \) from \( 3 \).
To perform this subtraction:
- Convert \( 3 \) to a fraction: \( 3 = \frac{12}{4} \).
- Now subtract \( \frac{1}{4} \):
\[ \frac{12}{4} - \frac{1}{4} = \frac{11}{4} \]
The slope of the line is \( \frac{11}{4} \).
Next, we need to find a table where the change in \( y \) divided by the change in \( x \) gives a slope of \( \frac{11}{4} \):
- The slope \( m \) is calculated as \( m = \frac{\Delta y}{\Delta x} \).
- To satisfy \( \frac{\Delta y}{\Delta x} = \frac{11}{4} \), the changes in both \( y \) and \( x \) must align such that when you take the ratio, you get \( \frac{11}{4} \).
Let's analyze the given tables:
-
Table 1: \[ x: 2 \quad 5 \ y: 4 \quad 1 \]
- \( \Delta y = 1 - 4 = -3 \)
- \( \Delta x = 5 - 2 = 3 \)
- Slope = \( \frac{-3}{3} = -1 \) (not \( \frac{11}{4} \))
-
Table 2: \[ x: 5 \quad 1 \ y: 4 \quad 2 \]
- \( \Delta y = 2 - 4 = -2 \)
- \( \Delta x = 1 - 5 = -4 \)
- Slope = \( \frac{-2}{-4} = \frac{1}{2} \) (not \( \frac{11}{4} \))
-
Table 3: \[ x: 2 \quad 4 \ y: 1 \quad 5 \]
- \( \Delta y = 5 - 1 = 4 \)
- \( \Delta x = 4 - 2 = 2 \)
- Slope = \( \frac{4}{2} = 2 \) (not \( \frac{11}{4} \))
-
Table 4: \[ x: 4 \quad 2 \ y: -5 \quad -1 \]
- \( \Delta y = -1 - (-5) = 4 \)
- \( \Delta x = 2 - 4 = -2 \)
- Slope = \( \frac{4}{-2} = -2 \) (not \( \frac{11}{4} \))
None of the tables directly show a slope of \( \frac{11}{4} \), but if we need to change our intervals or find values across a grid or a linear function linearly increasing with that slope, we need specific pairs that can be generated.
In conclusion, you might want to double-check the values available, or it's possible that no table represents Ava's line based on the simplified calculations from the slope expression.