Question

Ava wrote the expression 4−23−1 to determine the slope of a line. Which table might represent Ava’s line?(1 point)Responsesxy4321x y 4 3 2 1xy34-1-2x y 3 4 -1 -2xy1234 x y 1 2 3 4 xy4321x y 4 3 2 1

Answer 1

To determine the slope of a line from the expression 4 - 23 - 1, we first need to evaluate the expression correctly. It appears there may be a misunderstanding in interpreting the expression, as it lacks operators between terms. Assuming Ava intended to express a slope formula involving points, we can break down the possible slopes derived from the slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \).

Let's calculate the effective slope that Ava might be looking for by correcting the provided expression.

If we view the expression as a calculation involving constant values, we could suggest:
- Ava might be evaluating a slope such as \( m = 4 - (2 - 1) = 4 - 1 = 3 \).

Now, to find the correct table to represent a line with a slope of 3, we can use the general formula for lines, \( y = mx + b \). If we assume a y-intercept (b) of 0 for simplicity, the equation will be \( y = 3x \).

Let’s examine the given tables to check which fits this equation.

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

- Here, the slope between points (2, 1) and (4, 3) is calculated as:
\[
\text{slope} = \frac{3 - 1}{4 - 2} = \frac{2}{2} = 1 \quad (not \, 3)
\]

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

- Here, the slope between points (3, 4) and (-1, -2) is calculated as:
\[
\text{slope} = \frac{4 - (-2)}{3 - (-1)} = \frac{4 + 2}{3 + 1} = \frac{6}{4} = 1.5 \quad (not \, 3)
\]

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

- Here, the slope between points (1, 2) and (3, 4) is calculated as:
\[
\text{slope} = \frac{4 - 2}{3 - 1} = \frac{2}{2} = 1 \quad (not \, 3)
\]

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

- Repeating table 1, which we already calculated the slope for.

In conclusion, none of these tables directly represent a line with a slope of \(3\). If Ava’s vision was indeed to check for slope specifically as \(3\), tables representing the slope of \(3\) would need points consistent with the equation \( y = 3x \).

For example:
- If \( x = 0, y = 0 \)
- If \( x = 1, y = 3 \)
- If \( x = 2, y = 6 \)

If you have any more contexts or need me to calculate for different assumptions, feel free to ask!