Question
Which table of values corresponds to the graph below?
On a coordinate plane, a line goes through points (0, negative 2) and (2, 0).
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, negative 1, 0, 2. Column 2 is labeled y with entries 0, 1, 2, 4.
A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 1, 2, 4. Column 2 is labeled y with entries negative 2, negative 1, 2.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, 0, 1, 4. Column 2 is labeled y with entries 0, 2, negative 1, 2.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 0, 2, 4. Column 2 is labeled y with entries 1, negative 2, 0, 2.
On a coordinate plane, a line goes through points (0, negative 2) and (2, 0).
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, negative 1, 0, 2. Column 2 is labeled y with entries 0, 1, 2, 4.
A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 1, 2, 4. Column 2 is labeled y with entries negative 2, negative 1, 2.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, 0, 1, 4. Column 2 is labeled y with entries 0, 2, negative 1, 2.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 0, 2, 4. Column 2 is labeled y with entries 1, negative 2, 0, 2.
Answers
GPT-4o mini
To determine which table of values corresponds to the graph of the line that goes through the points (0, -2) and (2, 0), we first need to find the equation of the line.
1. **Calculate the slope (m)**:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-2)}{2 - 0} = \frac{2}{2} = 1
\]
2. **Use the point-slope form to find the equation of the line**:
Using the point (0, -2):
\[
y - y_1 = m(x - x_1) \implies y - (-2) = 1(x - 0) \implies y + 2 = x \implies y = x - 2
\]
3. **Create a table of values** using the equation \(y = x - 2\):
- For \(x = -2\): \(y = -2 - 2 = -4\)
- For \(x = -1\): \(y = -1 - 2 = -3\)
- For \(x = 0\): \(y = 0 - 2 = -2\)
- For \(x = 1\): \(y = 1 - 2 = -1\)
- For \(x = 2\): \(y = 2 - 2 = 0\)
- For \(x = 3\): \(y = 3 - 2 = 1\)
- For \(x = 4\): \(y = 4 - 2 = 2\)
Therefore, we can summarize the values:
```
| x | y |
|-------|-------|
| -2 | -4 |
| -1 | -3 |
| 0 | -2 |
| 1 | -1 |
| 2 | 0 |
| 3 | 1 |
| 4 | 2 |
```
Now, let's analyze the given tables:
1. The first table includes x-values of -2, -1, 0, and 2 but has y-values (0, 1, 2, 4) that do not correspond to the line equation \(y = x - 2\).
2. The second table includes x-values of 0, 1, 2, and 4, but the y-values (−2, −1, 2) are not correct either.
3. The third table includes x-values of -2, 0, 1, and 4 with corresponding y-values that do not fit the correct output from our line equation.
4. The fourth table includes values of \(x = -1, 0, 2, 4\) which also do not map correctly based on the line we determined.
After analyzing these tables and understanding the line through points (0, -2) and (2, 0), we find that none of the given tables correspond to the line equation \(y = x - 2\).
If you could share the exact values of the y-coordinate in the tables, I may provide a more precise analysis.
1. **Calculate the slope (m)**:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-2)}{2 - 0} = \frac{2}{2} = 1
\]
2. **Use the point-slope form to find the equation of the line**:
Using the point (0, -2):
\[
y - y_1 = m(x - x_1) \implies y - (-2) = 1(x - 0) \implies y + 2 = x \implies y = x - 2
\]
3. **Create a table of values** using the equation \(y = x - 2\):
- For \(x = -2\): \(y = -2 - 2 = -4\)
- For \(x = -1\): \(y = -1 - 2 = -3\)
- For \(x = 0\): \(y = 0 - 2 = -2\)
- For \(x = 1\): \(y = 1 - 2 = -1\)
- For \(x = 2\): \(y = 2 - 2 = 0\)
- For \(x = 3\): \(y = 3 - 2 = 1\)
- For \(x = 4\): \(y = 4 - 2 = 2\)
Therefore, we can summarize the values:
```
| x | y |
|-------|-------|
| -2 | -4 |
| -1 | -3 |
| 0 | -2 |
| 1 | -1 |
| 2 | 0 |
| 3 | 1 |
| 4 | 2 |
```
Now, let's analyze the given tables:
1. The first table includes x-values of -2, -1, 0, and 2 but has y-values (0, 1, 2, 4) that do not correspond to the line equation \(y = x - 2\).
2. The second table includes x-values of 0, 1, 2, and 4, but the y-values (−2, −1, 2) are not correct either.
3. The third table includes x-values of -2, 0, 1, and 4 with corresponding y-values that do not fit the correct output from our line equation.
4. The fourth table includes values of \(x = -1, 0, 2, 4\) which also do not map correctly based on the line we determined.
After analyzing these tables and understanding the line through points (0, -2) and (2, 0), we find that none of the given tables correspond to the line equation \(y = x - 2\).
If you could share the exact values of the y-coordinate in the tables, I may provide a more precise analysis.