Question

The table shows ordered pairs of the function y = 16 + 0.5x .

A 2-column table with 6 rows. The first column is labeled x with entries negative 4, negative 2, 0, 1, x, 10. The second column is labeled y with entries 14, 15, 16, 16.5, y, 21.
Which ordered pair could be the missing values represented by (x, y)?

(0, 18)
(5, 19.5)
(8, 20)
(10, 21.5)

Answer 1

To find the missing values (x, y) that satisfy the function \( y = 16 + 0.5x \), we can first calculate the y-values for the given x-values in the table and then determine which ordered pair could match the missing values.

1. For \( x = -4 \):
\[
y = 16 + 0.5(-4) = 16 - 2 = 14
\]
2. For \( x = -2 \):
\[
y = 16 + 0.5(-2) = 16 - 1 = 15
\]
3. For \( x = 0 \):
\[
y = 16 + 0.5(0) = 16 + 0 = 16
\]
4. For \( x = 1 \):
\[
y = 16 + 0.5(1) = 16 + 0.5 = 16.5
\]
5. Now let's find the missing \( y \) for \( x \):
\[
y = 16 + 0.5x
\]
6. For \( x = 10 \):
\[
y = 16 + 0.5(10) = 16 + 5 = 21
\]

Now we have all of the calculated y-values:
- For \( x = -4 \), \( y = 14 \)
- For \( x = -2 \), \( y = 15 \)
- For \( x = 0 \), \( y = 16 \)
- For \( x = 1 \), \( y = 16.5 \)
- For \( x = 10 \), \( y = 21 \)

Now let's evaluate the options given for the missing \( (x, y) \):

1. **(0, 18)**: For \( x = 0 \), \( y = 16 \). This does not match.
2. **(5, 19.5)**:
\[
y = 16 + 0.5(5) = 16 + 2.5 = 18.5 \text{ (not a match)}
\]
3. **(8, 20)**:
\[
y = 16 + 0.5(8) = 16 + 4 = 20 \text{ (this is a match)}
\]
4. **(10, 21.5)**: For \( x = 10 \), \( y = 21 \). This does not match.

The only ordered pair that could be the missing values represented by \( (x, y) \) is **(8, 20)**.