Choose the correct answers. (Each answer, 3 points)

1.019) 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 | 21 |
| 4 | 25 |
| 6 | 29 |
| 8 | 33 |
| 10 | 37 |

C.

| x | y |
|----|----|
| 2 | 18 |
| 4 | 19 |
| 6 | 20 |
| 8 | 21 |
| 10 | 22 |

D.

| x | y |
|----|----|
| 8 | 1 |
| 9 | -1 |
| 10 | -3 |
| 11 | -5 |
| 12 | -7 |

Substitute the x values from each table into the equation y = − 2 x + 17 and calculate the corresponding y values.
Compare the calculated y values with the y values provided in each table.
Identify the table where all pairs of ( x , y ) satisfy the equation.
Table D is the only table that satisfies the equation y = − 2 x + 17 , 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 ( x , y ) pair in the correct table, substituting the x value into the equation should yield the corresponding y value.

Checking Each Table Let's analyze each table to see if it satisfies the equation y = − 2 x + 17 .


Table A:

For x = 8 , y = − 2 ( 8 ) + 17 = − 16 + 17 = 1 . The table gives y = 13 , which is incorrect.
For x = 10 , y = − 2 ( 10 ) + 17 = − 20 + 17 = − 3 . The table gives y = 12 , which is incorrect. Since the first two entries are incorrect, we can conclude that Table A does not represent the equation.

Table B:

For x = 2 , y = − 2 ( 2 ) + 17 = − 4 + 17 = 13 . The table gives y = 21 , which is incorrect.
For x = 4 , y = − 2 ( 4 ) + 17 = − 8 + 17 = 9 . The table gives y = 25 , which is incorrect. Since the first two entries are incorrect, we can conclude that Table B does not represent the equation.

Table C:

For x = 2 , y = − 2 ( 2 ) + 17 = − 4 + 17 = 13 . The table gives y = 18 , which is incorrect.
For x = 4 , y = − 2 ( 4 ) + 17 = − 8 + 17 = 9 . The table gives y = 19 , which is incorrect. Since the first two entries are incorrect, we can conclude that Table C does not represent the equation.

Table D:

For x = 8 , y = − 2 ( 8 ) + 17 = − 16 + 17 = 1 . The table gives y = 1 , which is correct.
For x = 9 , y = − 2 ( 9 ) + 17 = − 18 + 17 = − 1 . The table gives y = − 1 , which is correct.
For x = 10 , y = − 2 ( 10 ) + 17 = − 20 + 17 = − 3 . The table gives y = − 3 , which is correct.
For x = 11 , y = − 2 ( 11 ) + 17 = − 22 + 17 = − 5 . The table gives y = − 5 , which is correct.
For x = 12 , y = − 2 ( 12 ) + 17 = − 24 + 17 = − 7 . The table gives y = − 7 , which is correct. All entries in Table D satisfy the equation, so Table D represents the equation.


Conclusion After checking each table, we find that only Table D satisfies the equation y = − 2 x + 17 for all given x and y values.

Examples
Understanding linear equations like y = − 2 x + 17 is crucial in many real-world scenarios. For instance, imagine a taxi service that charges a fixed fee of $17 and an additional 2 p er mi l e . T h ee q u a t i o n y = -2x + 17 co u l d re p rese n tt h e t o t a l cos t ( y ) f or a r i d eo f x$ miles, but in this case the slope would be positive. If instead you are given $17 to start with, but spend 2 p er mi l e , t h ee q u a t i o n w o u l d a cc u r a t e l yre p rese n t h o w m u c hm o n eyyo u ha v e l e f t a f t er x$ miles. Identifying the correct table helps in predicting costs, managing budgets, or understanding relationships between variables in various situations.

Answered by GinnyAnswer | 2025-07-08

After evaluating each table against the equation y = − 2 x + 17 , it is found that only Table D accurately represents the equation for all its entries. Thus, the correct answer is D.
;

Answered by Anonymous | 2025-07-10