Which table shows ordered pairs that satisfy the function $y=2x+1$?
A.
| x | y |
|---|---|
| 0 | -2 |
| 1 | 4 |
| 2 | 6 |
B.
| x | y |
|---|---|
| 0 | 1 |
| 1 | 3 |
| 2 | 5 |
C.
| x | y |
|---|---|
| 0 | -1 |
| 1 | 0 |
| 2 | 1 |
D.
| x | y |
|---|---|
| 0 | -2 |
| 1 | 0 |
| 2 | 2 |
Answer (2)
Substitute the x values from each table into the equation y = 2 x + 1 and check if the resulting y value matches the y value in the table.
Table A does not satisfy the equation.
Table B satisfies the equation.
Therefore, the answer is Table B: B .
Explanation
Understanding the Problem We are given the function y = 2 x + 1 and four tables of ordered pairs. Our goal is to determine which table contains ordered pairs that satisfy the given function. To do this, we will substitute the x values from each table into the equation and check if the resulting y value matches the y value in the table.
Analyzing Table A Let's analyze Table A. The ordered pairs are (0, -2), (1, 4), and (2, 6). For x = 0 , y = 2 ( 0 ) + 1 = 1 . The table shows y = − 2 , so this pair does not satisfy the equation. For x = 1 , y = 2 ( 1 ) + 1 = 3 . The table shows y = 4 , so this pair does not satisfy the equation. For x = 2 , y = 2 ( 2 ) + 1 = 5 . The table shows y = 6 , so this pair does not satisfy the equation. Table A does not satisfy the equation.
Analyzing Table B Now, let's analyze Table B. The ordered pairs are (0, 1), (1, 3), and (2, 5). For x = 0 , y = 2 ( 0 ) + 1 = 1 . The table shows y = 1 , so this pair satisfies the equation. For x = 1 , y = 2 ( 1 ) + 1 = 3 . The table shows y = 3 , so this pair satisfies the equation. For x = 2 , y = 2 ( 2 ) + 1 = 5 . The table shows y = 5 , so this pair satisfies the equation. Table B satisfies the equation.
Analyzing Table C Let's analyze Table C. The ordered pairs are (0, -1), (1, 0), and (2, 1). For x = 0 , y = 2 ( 0 ) + 1 = 1 . The table shows y = − 1 , so this pair does not satisfy the equation. For x = 1 , y = 2 ( 1 ) + 1 = 3 . The table shows y = 0 , so this pair does not satisfy the equation. For x = 2 , y = 2 ( 2 ) + 1 = 5 . The table shows y = 1 , so this pair does not satisfy the equation. Table C does not satisfy the equation.
Analyzing Table D Finally, let's analyze Table D. The ordered pairs are (0, -2), (1, 0), and (2, 2). For x = 0 , y = 2 ( 0 ) + 1 = 1 . The table shows y = − 2 , so this pair does not satisfy the equation. For x = 1 , y = 2 ( 1 ) + 1 = 3 . The table shows y = 0 , so this pair does not satisfy the equation. For x = 2 , y = 2 ( 2 ) + 1 = 5 . The table shows y = 2 , so this pair does not satisfy the equation. Table D does not satisfy the equation.
Conclusion Only Table B contains ordered pairs that satisfy the equation y = 2 x + 1 . Therefore, the answer is Table B.
Examples
Understanding linear functions like y = 2 x + 1 is crucial in many real-world applications. For instance, consider a taxi fare that starts with a $1 initial charge and adds $2 for every mile traveled. Here, x represents the number of miles, and y represents the total fare. If you travel 3 miles, the fare would be $y = 2(3) + 1 = $7. This concept extends to budgeting, where you might have a fixed monthly expense plus a variable cost per item, or in physics, where you calculate distance based on a constant speed and initial position. Recognizing and applying linear functions helps in making informed decisions and predictions in everyday scenarios.
Only Table B contains ordered pairs that satisfy the equation y = 2 x + 1 . By substituting the x values from Table B into the equation, we confirm that all y values match. Thus, the correct option is Table B: B .
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