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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

5 answers

(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.

for question b, is it the y line or the x line?

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.

What is the answer of question (a)

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).