Question

If the set of values in the table represents points on a line, what is the missing value in the table?(1 point) x y -4 -1 2 2 4 8 5

Answer 1

To determine the missing value in the table and find the relationship between the \(x\) and \(y\) values, let's first list the given pairs of \(x\) and \(y\):

- For \(x = -4\), \(y = -1\)
- For \(x = 2\), \(y = 2\)
- For \(x = 4\), \(y = 8\)
- For \(x = 5\), \(y = ?\)

Next, we will check for a pattern or linear relationship among the given coordinates.

We can also calculate the slope (change in \(y\) divided by the change in \(x\)) between any two points to see if the slope is constant.

1. Between \((-4, -1)\) and \((2, 2)\):
\[
\text{slope} = \frac{2 - (-1)}{2 - (-4)} = \frac{2 + 1}{2 + 4} = \frac{3}{6} = \frac{1}{2}
\]

2. Between \((2, 2)\) and \((4, 8)\):
\[
\text{slope} = \frac{8 - 2}{4 - 2} = \frac{6}{2} = 3
\]
The slope has changed from \(\frac{1}{2}\) to \(3\), indicating these points may not lie on a single linear function. Let's check all points together to see if a consistent formula emerges.

Let’s look for a potential linear equation by considering \(y = mx + b\). We can derive the equation with any two known points.

Using \((2, 2)\) and \((4, 8)\):
\[
y = 3x - 4
\]
To find the \(y\) value for \(x = 5\):
\[
y = 3(5) - 4 = 15 - 4 = 11
\]

Thus, the missing value when \(x = 5\) is \(y = 11\). The completed table would look like this:

\[
\begin{array}{c|c}
x & y \\
\hline
-4 & -1 \\
2 & 2 \\
4 & 8 \\
5 & 11 \\
\end{array}
\]

Therefore, the missing value is **11**.