Question

Ava wrote the expression 4−12−3 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 -2xy4321x y 4 3 2 1xy3124

Answer 1

To determine which table might represent Ava's line based on the expression \( 4 - 12 - 3 \), we first need to simplify the expression:

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

This expression does not directly relate to the slope of a line unless we consider the numbers individually. However, if we interpret the operation as representing a slope, we can compute the slope from two points in a table.

The slope formula is given by:

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

Since Ava's expression evaluates to -11, we'll look for pairs of (x, y) that have a slope of -11.

Now let's analyze the response options:

1. **Table:**
\[
\begin{array}{c|c}
x & y \\
\hline
4 & 3 \\
2 & 1 \\
\end{array}
\]

- Slope Calculation:
\[
\text{slope} = \frac{1 - 3}{2 - 4} = \frac{-2}{-2} = 1 \quad (\text{Not } -11)
\]

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

- Slope Calculation:
\[
\text{slope} = \frac{-2 - 4}{-1 - 3} = \frac{-6}{-4} = \frac{3}{2} \quad (\text{Not } -11)
\]

3. **Table:**
\[
\begin{array}{c|c}
x & y \\
\hline
4 & 3 \\
2 & 1 \\
\end{array}
\]

(This is the same as the first table.)

4. **Table:**
\[
\begin{array}{c|c}
x & y \\
\hline
3 & 1 \\
2 & 4 \\
\end{array}
\]

- Slope Calculation:
\[
\text{slope} = \frac{4 - 1}{2 - 3} = \frac{3}{-1} = -3 \quad (\text{Not } -11)
\]

Based on the provided choices, none give a slope of -11, which would require examining points specifically for this slope.

Thus, Ava might need to choose a table that yields a slope of -11 or apply her calculations to find the corresponding values.

Assuming your inquiry aims at determining a table from those options, the tables presented do not yield a slope of -11. Therefore, if she was looking for one that represents the necessary slope, none match this criteria directly.