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 find the missing value of \( y \) when \( x = 4 \) in the table, we need to determine if the points \((-4, -1)\), \((2, 2)\), \((4, ?)\), and \((8, 5)\) are indeed on a straight line. This can be confirmed by calculating the slopes between the points and ensuring they are the same.

First, let's calculate the slope between the first two points \((-4, -1)\) and \((2, 2)\):

\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - (-1)}{2 - (-4)} = \frac{2 + 1}{2 + 4} = \frac{3}{6} = \frac{1}{2}
\]

Now calculate the slope between the second point \((2, 2)\) and the fourth point \((8, 5)\):

\[
\text{slope} = \frac{5 - 2}{8 - 2} = \frac{3}{6} = \frac{1}{2}
\]

The slopes between the points are consistent, both being \(\frac{1}{2}\). Now we can use this slope to find the missing \( y \) value for \( x = 4 \).

Using the point \((2, 2)\) and applying the slope \(\frac{1}{2}\) to find \( y \) when \( x = 4\):

\[
y - 2 = \frac{1}{2}(4 - 2)
\]

Calculating this gives:

\[
y - 2 = \frac{1}{2} \cdot 2 = 1
\]

Adding 2 to both sides:

\[
y = 1 + 2 = 3
\]

Thus, the missing value in the table when \( x = 4 \) is:

\[
\boxed{3}
\]