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In Mathematics / High School | 2025-07-03

The table shows ordered pairs of the function [tex]$y=16+0.5 x$[/tex].

Which ordered pair could be the missing values represented by [tex]$(x, y)$[/tex]?

[tex]$(0,18)$[/tex]
[tex]$(5,19.5)$[/tex]
[tex]$(8,20)$[/tex]
[tex]$(10,21.5)$[/tex]

Asked by boiwhat039

Answer (2)

Substitute each x-value from the ordered pairs into the equation y = 16 + 0.5 x .
Calculate the corresponding y-value for each x-value.
Compare the calculated y-value with the given y-value in the ordered pair.
The ordered pair ( 8 , 20 ) is the only one that satisfies the equation, so the answer is ( 8 , 20 ) ​ .

Explanation

Understanding the Problem We are given the function y = 16 + 0.5 x and a table of ordered pairs. We need to determine which of the given ordered pairs satisfies the equation.

Solution Plan We will test each ordered pair ( x , y ) to see if it satisfies the equation y = 16 + 0.5 x .

Testing the Ordered Pairs

Test ( 0 , 18 ) : If x = 0 , then y = 16 + 0.5 ( 0 ) = 16 + 0 = 16 . Since 16 e q 18 , this ordered pair is not a solution.

Test ( 5 , 19.5 ) : If x = 5 , then y = 16 + 0.5 ( 5 ) = 16 + 2.5 = 18.5 . Since 18.5 e q 19.5 , this ordered pair is not a solution.

Test ( 8 , 20 ) : If x = 8 , then y = 16 + 0.5 ( 8 ) = 16 + 4 = 20 . Since 20 = 20 , this ordered pair is a solution.

Test ( 10 , 21.5 ) : If x = 10 , then y = 16 + 0.5 ( 10 ) = 16 + 5 = 21 . Since 21 e q 21.5 , this ordered pair is not a solution.

Final Answer The ordered pair ( 8 , 20 ) satisfies the equation y = 16 + 0.5 x .


Examples
Understanding linear functions like y = 16 + 0.5 x is useful in many real-world situations. For example, a taxi fare might be calculated as a base fee of $16 plus $0.5 per mile. If you travel 8 miles, the fare would be $16 + 0.5 \times 8 = $20. This kind of calculation helps you estimate costs and plan your budget effectively.

Answered by GinnyAnswer | 2025-07-03

The ordered pair that satisfies the equation y = 16 + 0.5 x is ( 8 , 20 ) . All other pairs do not meet the condition of the equation. Thus, ( 8 , 20 ) is the correct answer.
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Answered by Anonymous | 2025-07-04

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