Question

Ava wrote the expression (4−1)/(2−3)
to determine the slope of a line. Which table might represent Ava’s line?(1 point)
Responses

x y
3 4
-1 -2


x y
4 3
2 1


x y
3 1
2 4



x y
4 3
2 1

Answer 1

To determine the slope from Ava's expression \((4−1)/(2−3)\), we can simplify the expression:

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

The slope of the line is \(-3\).

Now, to find a table that represents a line with a slope of \(-3\), we will check if we can find two points in one of the tables that have a slope of \(-3\). The slope \(-3\) means that for every 1 unit increase in \(x\), \(y\) will decrease by 3 units.

Let's examine the provided tables:

1. Table:
\[
\begin{array}{c|c}
x & y \\
\hline
3 & 4 \\
-1 & -2 \\
\end{array}
\]
The slope between (3, 4) and (-1, -2) is:
\[
\text{slope} = \frac{-2 - 4}{-1 - 3} = \frac{-6}{-4} = \frac{3}{2} \quad \text{(not -3)}
\]

2. Table:
\[
\begin{array}{c|c}
x & y \\
\hline
4 & 3 \\
2 & 1 \\
\end{array}
\]
The slope between (4, 3) and (2, 1) is:
\[
\text{slope} = \frac{1 - 3}{2 - 4} = \frac{-2}{-2} = 1 \quad \text{(not -3)}
\]

3. Table:
\[
\begin{array}{c|c}
x & y \\
\hline
3 & 1 \\
2 & 4 \\
\end{array}
\]
The slope between (3, 1) and (2, 4) is:
\[
\text{slope} = \frac{4 - 1}{2 - 3} = \frac{3}{-1} = -3 \quad \text{(correct)}
\]

4. (Duplicate of the second table given previously)

The table that represents Ava's line with a slope of \(-3\) is:

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

So the answer is the third table.