Choose the correct answer. Which table represents the equation [tex]y=-2 x+17[/tex]?
A.
| x | y |
| --- | --- |
| 8 | 13 |
| 10 | 12 |
| 12 | 11 |
| 14 | 10 |
| 16 | 9 |
B.
| x | y |
| --- | --- |
| 2 | 18 |
| 4 | 19 |
| 6 | 20 |
| 8 | 21 |
| 10 | 22 |
C.
| x | y |
| --- | --- |
| 2 | 21 |
| 4 | 25 |
| 6 | 29 |
| 8 | 33 |
| 10 | 37 |
D.
| x | y |
| --- | --- |
| 8 | 1 |
| 9 | -1 |
| 10 | -3 |
| 11 | -5 |
| 12 | -7 |
Answer (2)
Substitute the x values from each table into the equation y = − 2 x + 17 and compare the result with the corresponding y values in the table.
Table A, B, and C do not satisfy the equation for all pairs of ( x , y ) .
Table D satisfies the equation for all pairs of ( x , y ) .
The correct table is D, so the answer is D .
Explanation
Understanding the Problem We are given the equation y = − 2 x + 17 and four tables of x and y values. Our goal is to determine which table satisfies the given equation. This means that for each pair of ( x , y ) in the correct table, when we substitute the x value into the equation, we should obtain the corresponding y value.
Checking the Tables Let's examine each table to see if the values satisfy the equation y = − 2 x + 17 .
Verifying the Tables Table A: For x = 8 , y = − 2 ( 8 ) + 17 = − 16 + 17 = 1 . The table gives y = 13 , which does not match. So, Table A is incorrect. Table B: For x = 2 , y = − 2 ( 2 ) + 17 = − 4 + 17 = 13 . The table gives y = 18 , which does not match. So, Table B is incorrect. Table C: For x = 2 , y = − 2 ( 2 ) + 17 = − 4 + 17 = 13 . The table gives y = 21 , which does not match. So, Table C is incorrect. Table D: For x = 8 , y = − 2 ( 8 ) + 17 = − 16 + 17 = 1 . The table gives y = 1 , which matches. For x = 9 , y = − 2 ( 9 ) + 17 = − 18 + 17 = − 1 . The table gives y = − 1 , which matches. For x = 10 , y = − 2 ( 10 ) + 17 = − 20 + 17 = − 3 . The table gives y = − 3 , which matches. For x = 11 , y = − 2 ( 11 ) + 17 = − 22 + 17 = − 5 . The table gives y = − 5 , which matches. For x = 12 , y = − 2 ( 12 ) + 17 = − 24 + 17 = − 7 . The table gives y = − 7 , which matches. Since all pairs in Table D satisfy the equation, Table D is the correct table.
Final Answer Therefore, the correct answer is Table D.
Examples
Understanding linear equations like y = − 2 x + 17 is crucial in many real-world scenarios. For example, imagine a taxi service charges a fixed fee of $17 and an additional 2 f ore v ery mi l e t r a v e l e d . T h ee q u a t i o n y = -2x + 17 co u l d re p rese n tt h e t o t a l cos t ( y$) if you are getting a discount of 2 p er mi l e ( x$) from a base cost of $17. Identifying the correct table helps in predicting costs accurately based on distance.
We evaluated the x values from each table using the equation y = − 2 x + 17 . Table D is the only one where all pairs of ( x , y ) values satisfy the equation. Thus, the answer is Table D.
;
