Question

Ava wrote the expression 5−14−2
to determine the slope of a line. Which table might represent Ava’s line?(1 point)
Responses

x y
2 1
4 5


x y 2 1 4 5

x y
5 4
1 2
x y 5 4 1 2

x y
2 5
4 1
x y 2 5 4 1

x y
4 -5
2 -1

Answer 1

whats the closeat answer

Answer 2

To determine which table might represent Ava's line, we need to find the slope based on her expression \(5 - 14 - 2\).

Let's simplify that expression:
- \(5 - 14 = -9\)
- \(-9 - 2 = -11\)

Therefore, the slope of the line Ava is looking for is \(-11\).

Now, we'll check the slope between the points in each table. The slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:

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

### Table 1
\[
\begin{align*}
(x, y) & : (2, 1) \\
(x, y) & : (4, 5)
\end{align*}
\]
Calculating the slope:
\[
\text{slope} = \frac{5 - 1}{4 - 2} = \frac{4}{2} = 2
\]

### Table 2
\[
\begin{align*}
(x, y) & : (5, 4) \\
(x, y) & : (1, 2)
\end{align*}
\]
Calculating the slope:
\[
\text{slope} = \frac{2 - 4}{1 - 5} = \frac{-2}{-4} = \frac{1}{2}
\]

### Table 3
\[
\begin{align*}
(x, y) & : (2, 5) \\
(x, y) & : (4, 1)
\end{align*}
\]
Calculating the slope:
\[
\text{slope} = \frac{1 - 5}{4 - 2} = \frac{-4}{2} = -2
\]

### Table 4
\[
\begin{align*}
(x, y) & : (4, -5) \\
(x, y) & : (2, -1)
\end{align*}
\]
Calculating the slope:
\[
\text{slope} = \frac{-1 + 5}{2 - 4} = \frac{4}{-2} = -2
\]

After evaluating the slopes from all the tables, none match the calculated slope of \(-11\). It suggests that there might be some confusion regarding the points that would lead to a slope of \(-11\).

To find pairs of points that yield a slope of \(-11\), you can work backward.

Using the slope formula to find new pairs:

From \(y - y_1 = m(x - x_1)\) where \(m = -11\):

Let’s say we have a point \((x_1, y_1)\) and want to find a point with \(x_2\):

\[
y_2 = y_1 - 11(x_2 - x_1)
\]

You can substitute different values for \(x_2\) and for points that Ava may have chosen to get a slope of \(-11\).

Thus, based on the calculations, **none of the provided tables represent Ava's line correctly with the slope of \(-11\)**.

Answer 3

To determine which table might represent Ava’s line, we calculated the slopes from each table to see if any of them are close to \(-11\).

Here's a recap of the slopes we calculated:

1. **Table 1:**
- Points: (2, 1) and (4, 5)
- Slope: 2

2. **Table 2:**
- Points: (5, 4) and (1, 2)
- Slope: 0.5

3. **Table 3:**
- Points: (2, 5) and (4, 1)
- Slope: -2

4. **Table 4:**
- Points: (4, -5) and (2, -1)
- Slope: -2

None of the calculated slopes match the desired slope of \(-11\). However, since you're asking for the closest answer, let's review the slopes again. The closest value to -11 in the slope calculation is **-2**, found in **Table 3** and **Table 4**.

If I needed to pick the closest table based on the negative slope, I would go with **either Table 3 or Table 4**, as both have a slope of -2.

Since they both have the same slope, you can choose either one as the closest option since they are both equally far from \(-11\).