Question

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

$x$	$y$
$-2$	$15$
$0$	$16$
$1$	$16.5$
$x$	$y$
$10$	$21$

which ordered pair could be the missing values represented by $(x, y)$?

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

Explanation:

Step1: Recall the function

The function is \( y = 16 + 0.5x \). We need to check each option by substituting \( x \) into the function and see if we get the corresponding \( y \).

Step2: Check option (0, 18)

Substitute \( x = 0 \) into \( y = 16 + 0.5x \):
\( y = 16 + 0.5(0) = 16 \). But the option has \( y = 18 \), so this is incorrect.

Step3: Check option (8, 20)

Substitute \( x = 8 \) into \( y = 16 + 0.5x \):
\( y = 16 + 0.5(8) = 16 + 4 = 20 \). This matches the \( y \)-value in the option. Let's check the other options to be sure.

Step4: Check option (10, 21.5)

From the table, when \( x = 10 \), \( y = 21 \). Substituting \( x = 10 \) into the function: \( y = 16 + 0.5(10) = 16 + 5 = 21 \), not \( 21.5 \). So this is incorrect.

Step5: Check option (5, 19.5)

Substitute \( x = 5 \) into \( y = 16 + 0.5x \):
\( y = 16 + 0.5(5) = 16 + 2.5 = 18.5 \), not \( 19.5 \). So this is incorrect.

Answer:

(8, 20)