Question

Ava wrote the expression 4−12−3
to determine the slope of a line. Which table might represent Ava’s line?(1 point)
Responses

x y
3 1
2 4


x y 3 1 2 4

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

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

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

Answer 1

To determine which table might represent Ava's line, we first need to clarify the expression Ava wrote, which is \(4 - 12 - 3\). This expression simplifies to:

\[
4 - 12 - 3 = 4 - 15 = -11
\]

However, it seems more likely that Ava intended to find the slope of the line, potentially using a different set of numbers or context. To find the slope (m), we need two points from the tables and then calculate the slope using the formula:

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

Now, let's analyze the tables provided to see if any of them represent lines with a consistent slope:

1. **Table 1:**
\[
\begin{array}{c|c}
x & y \\
\hline
3 & 1 \\
2 & 4 \\
\end{array}
\]
- Slope calculation:
\[
m = \frac{4 - 1}{2 - 3} = \frac{3}{-1} = -3
\]

2. **Table 2:**
\[
\begin{array}{c|c}
x & y \\
\hline
3 & 4 \\
-1 & -2 \\
\end{array}
\]
- Slope calculation:
\[
m = \frac{-2 - 4}{-1 - 3} = \frac{-6}{-4} = \frac{3}{2}
\]

3. **Table 3:** (same as Table 4)
\[
\begin{array}{c|c}
x & y \\
\hline
4 & 3 \\
2 & 1 \\
\end{array}
\]
- Slope calculation:
\[
m = \frac{1 - 3}{2 - 4} = \frac{-2}{-2} = 1
\]

Now let's recap the slopes we calculated for the tables:
- Table 1: slope of -3
- Table 2: slope of \( \frac{3}{2} \)
- Table 3 and 4: slope of 1

Given that the slope was determined in the context of \(4 - 12 - 3\) resulting in -11 and was likely part of a different exercise, the most consistent representation of a line might be with the slope of -3 (as negative slopes could relate to a downward trend).

If your question was specifically about which of the tables could be related to a slope based on Ava's expression, normally we would be looking for either negative or positive slopes depending on her earlier calculations. From the choices available without additional clarifying criteria, **Table 1** would have a consistent downward slope (negative slope).

So, the answer may be interpreted based on the context, but if focusing strictly on slopes derived from the tables:
**Table 1** could represent a line that relates to a negative slope.