Question

Ava wrote the expression 4−23−1
to determine the slope of a line. Which table might represent Ava’s line?(1 point)
Responses

x y
4 3
2 1
x y 4 3 2 1

x y
3 4
-1 -2
x y 3 4 -1 -2

x y
1 2
3 4


x y 1 2 3 4

x y
4 3
2 1
x y 4 3 2 1

Answer 1

To determine which table might represent Ava's line based on the expression \( 4 - 2 \cdot 3 - 1 \), we first need to understand what slope means in the context of a line. The slope \( m \) is calculated using two points \((x_1, y_1)\) and \((x_2, y_2)\) on the line as follows:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

From Ava's expression \( 4 - 2\cdot 3 - 1 \), it seems she is most likely misunderstanding the formula for slope. However, if we simply consider the outcome and look for a line with a slope based on that outcome, we can check the provided tables.

Let's look at the first response (which appears to be repeated):

1. **Table:**
```
x y
4 3
2 1
```

Using the points (4, 3) and (2, 1):

\[
m = \frac{1 - 3}{2 - 4} = \frac{-2}{-2} = 1
\]

2. **Table:**
```
x y
3 4
-1 -2
```

Using the points (3, 4) and (-1, -2):

\[
m = \frac{-2 - 4}{-1 - 3} = \frac{-6}{-4} = \frac{3}{2}
\]

3. **Table:**
```
x y
1 2
3 4
```

Using the points (1, 2) and (3, 4):

\[
m = \frac{4 - 2}{3 - 1} = \frac{2}{2} = 1
\]

4. **Table:**
```
x y
4 3
2 1
```

This is identical to the first table, and we already calculated the slope \( m = 1 \).

After checking all possibilities, the tables that yield a slope of 1 are the first table and the third table. The first table appears twice. Therefore, any line represented in either of these tables could correspond to Ava's expression incorrectly interpreted for slope.

**Final Answer:** The first table and the third table both represent lines with a slope of 1. The repeated first table is a correct choice.