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 if the given points represent a line, we can check for a consistent slope between the pairs of points.

1. First, let's calculate the slope (m) between the first pair of points: (-4, -1) and (2, 2).
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - (-1)}{2 - (-4)} = \frac{3}{6} = \frac{1}{2}
\]

2. Next, let's check the slope between the second pair of points: (2, 2) and (4, y).
We can use the slope we found (1/2) to find y.
The general formula for slope is:
\[
m = \frac{y - 2}{4 - 2} = \frac{y - 2}{2}
\]
Setting this equal to the known slope:
\[
\frac{y - 2}{2} = \frac{1}{2}
\]

Cross-multiplying gives:
\[
y - 2 = 1 \implies y = 3
\]

3. Now, we have the coordinates for the third point: (4, 3).

4. Finally, let's check the slope between the point (4, 3) and (8, y):
\[
\frac{y - 3}{8 - 4} = \frac{y - 3}{4}
\]
Again setting this equal to the slope (1/2):
\[
\frac{y - 3}{4} = \frac{1}{2}
\]

Cross-multiplying gives:
\[
y - 3 = 2 \implies y = 5
\]

Thus, the missing value in the table for the fourth point (8, y) is:
\[
\boxed{5}
\]