To find a point on the line that passes through (0, 6) and is parallel to the given line, we first need to determine the slope of the given line. We can do this by using the points provided.
The coordinates of the given points are (12, 8), (6, 6), (2, 8), and (6, 0). Let’s first calculate the slope between the points (12, 8) and (6, 6):
Slope (m) = (y2 – y1) / (x2 – x1) = (6 – 8) / (6 – 12) = (-2) / (-6) = 1/3.
This slope tells us that for every 3 units we move horizontally to the right, we move 1 unit vertically up. Since we want a line that is parallel to this one, it will have the same slope of 1/3.
Now, the line passing through (0, 6) with this slope can be described by the point-slope form of the linear equation. So we can use:
y – y1 = m(x – x1),
where (x1, y1) is the point (0, 6) and m is the slope (1/3).
Substituting these values gives:
y – 6 = (1/3)(x – 0),
which simplifies to:
y = (1/3)x + 6.
To find a specific point on this line, we can choose any x-value. For example, let’s choose x = 3.
Substituting x = 3 into the equation:
y = (1/3)(3) + 6 = 1 + 6 = 7.
Thus, the point (3, 7) lies on the line that passes through (0, 6) and is parallel to the line defined by the given points. Therefore, one possible answer for a point on this parallel line is (3, 7).