Question

Ava wrote the expression 5−1/4−2 to determine the slope of a line. Which table might represent Ava’s line?(1 point)
Responses
xy 2 5 4 1


x y 5 4 1 2

 
x y 2 1 4 5  
x y 4 -5 2-1

Answer 1

To determine the slope from Ava's expression \( 5 - \frac{1}{4} - 2 \), we first simplify it.

1. Start with \( 5 - 2 = 3 \).
2. 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:

1. **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 \( \frac{11}{4} \))

2. **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 \( \frac{11}{4} \))

3. **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 \( \frac{11}{4} \))

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.