Question
answer the questions below.
Refer to the equation 2x - 6y + 12.
(a) Create a table of values for at least 4 points. Show your work
(b) Use the table of values to graph the line
Say the answer in bold font
Refer to the equation 2x - 6y + 12.
(a) Create a table of values for at least 4 points. Show your work
(b) Use the table of values to graph the line
Say the answer in bold font
Answers
GPT-4o mini
**(a) To create a table of values for the equation 2x - 6y + 12 = 0, we will first rearrange the equation to solve for y.**
Starting with the original equation:
\[ 2x - 6y + 12 = 0 \]
Rearranging gives:
\[ -6y = -2x - 12 \]
Dividing by -6:
\[ y = \frac{1}{3}x + 2 \]
Now we can create a table of values by choosing different values for x and calculating the corresponding y values.
| x | y |
|-----|-------|
| -6 | 0 | (When x = -6, y = \frac{1}{3}(-6) + 2 = -2 + 2 = 0) |
| 0 | 2 | (When x = 0, y = \frac{1}{3}(0) + 2 = 0 + 2 = 2) |
| 6 | 4 | (When x = 6, y = \frac{1}{3}(6) + 2 = 2 + 2 = 4) |
| 12 | 6 | (When x = 12, y = \frac{1}{3}(12) + 2 = 4 + 2 = 6) |
**(b) Using the table of values, we can now graph the line.**
To graph the line, plot the points \((-6, 0)\), \((0, 2)\), \((6, 4)\), and \((12, 6)\) on a coordinate plane. Connect the points with a straight line to represent the linear equation \(2x - 6y + 12 = 0\).
The final graph should show a straight line going through these points with a positive slope (since the coefficient of x is positive).
**In summary, the points are (-6, 0), (0, 2), (6, 4), and (12, 6). The graph is a straight line that passes through these points.**
Starting with the original equation:
\[ 2x - 6y + 12 = 0 \]
Rearranging gives:
\[ -6y = -2x - 12 \]
Dividing by -6:
\[ y = \frac{1}{3}x + 2 \]
Now we can create a table of values by choosing different values for x and calculating the corresponding y values.
| x | y |
|-----|-------|
| -6 | 0 | (When x = -6, y = \frac{1}{3}(-6) + 2 = -2 + 2 = 0) |
| 0 | 2 | (When x = 0, y = \frac{1}{3}(0) + 2 = 0 + 2 = 2) |
| 6 | 4 | (When x = 6, y = \frac{1}{3}(6) + 2 = 2 + 2 = 4) |
| 12 | 6 | (When x = 12, y = \frac{1}{3}(12) + 2 = 4 + 2 = 6) |
**(b) Using the table of values, we can now graph the line.**
To graph the line, plot the points \((-6, 0)\), \((0, 2)\), \((6, 4)\), and \((12, 6)\) on a coordinate plane. Connect the points with a straight line to represent the linear equation \(2x - 6y + 12 = 0\).
The final graph should show a straight line going through these points with a positive slope (since the coefficient of x is positive).
**In summary, the points are (-6, 0), (0, 2), (6, 4), and (12, 6). The graph is a straight line that passes through these points.**
for question b, is it the y line or the x line?
GPT-4o mini
**In question (b), the graph represents the line for the given equation \(2x - 6y + 12 = 0\), which is plotted on a coordinate plane with both the x-axis (horizontal) and the y-axis (vertical).**
The line itself would cross the y-axis at (0, 2) and the x-axis at (-6, 0). Therefore, it is not solely a vertical or horizontal line; it has a slope that allows it to rise from left to right, indicating a positive relationship between x and y.
In summary, the graph includes both axes and depicts the relationship defined by the equation. **The line is neither exclusively the x-axis nor the y-axis, but a linear representation of the relationship between x and y as determined by the equation.**
The line itself would cross the y-axis at (0, 2) and the x-axis at (-6, 0). Therefore, it is not solely a vertical or horizontal line; it has a slope that allows it to rise from left to right, indicating a positive relationship between x and y.
In summary, the graph includes both axes and depicts the relationship defined by the equation. **The line is neither exclusively the x-axis nor the y-axis, but a linear representation of the relationship between x and y as determined by the equation.**
What is the answer of question (a)
GPT-4o mini
**The answer to question (a) is the table of values created from the equation \(2x - 6y + 12 = 0\). Here's the table of values once again:**
| x | y |
|-----|-------|
| -6 | 0 | (*When x = -6: \(y = \frac{1}{3}(-6) + 2 = 0\)*) |
| 0 | 2 | (*When x = 0: \(y = \frac{1}{3}(0) + 2 = 2\)*) |
| 6 | 4 | (*When x = 6: \(y = \frac{1}{3}(6) + 2 = 4\)*) |
| 12 | 6 | (*When x = 12: \(y = \frac{1}{3}(12) + 2 = 6\)*) |
**Thus, the points that can be plotted based on this table are: (-6, 0), (0, 2), (6, 4), and (12, 6).**
| x | y |
|-----|-------|
| -6 | 0 | (*When x = -6: \(y = \frac{1}{3}(-6) + 2 = 0\)*) |
| 0 | 2 | (*When x = 0: \(y = \frac{1}{3}(0) + 2 = 2\)*) |
| 6 | 4 | (*When x = 6: \(y = \frac{1}{3}(6) + 2 = 4\)*) |
| 12 | 6 | (*When x = 12: \(y = \frac{1}{3}(12) + 2 = 6\)*) |
**Thus, the points that can be plotted based on this table are: (-6, 0), (0, 2), (6, 4), and (12, 6).**