Find the slope of this following line: (-2, 6), (2, -2)

To find the slope of a line passing through two points, we can use the slope formula:

slope = (difference in y-coordinates) / (difference in x-coordinates)

Let's call the coordinates of the first point (x₁, y₁) and the coordinates of the second point (x₂, y₂). In this case, the coordinates are (-2, 6) for the first point and (2, -2) for the second point.

Using the formula, we can calculate the slope:

slope = (6 - (-2)) / (-2 - 2)
slope = (6 + 2) / (-4)
slope = 8 / -4
slope = -2

Therefore, the slope of the line passing through the points (-2, 6) and (2, -2) is -2.

(-7, -4), (-7, -5)

To find the slope of the line passing through the points (-7, -4) and (-7, -5), we can use the slope formula:

slope = (difference in y-coordinates) / (difference in x-coordinates)

Let's call the coordinates of the first point (x₁, y₁) and the coordinates of the second point (x₂, y₂). In this case, the coordinates are (-7, -4) for the first point and (-7, -5) for the second point.

Using the formula, we can calculate the slope:

slope = (-5 - (-4)) / (-7 - (-7))
slope = (-5 + 4) / (-7 + 7)
slope = -1 / 0

The difference in x-coordinates is 0, which means the denominator is 0. Dividing by 0 is undefined, so the slope of the line passing through the points (-7, -4) and (-7, -5) does not exist. This means the line is vertically oriented and parallel to the y-axis.

What about: (2, 4), (6, 6)

To find the slope of the line passing through the points (2, 4) and (6, 6), we can use the slope formula:

slope = (difference in y-coordinates) / (difference in x-coordinates)

The coordinates of the first point are (x₁, y₁) = (2, 4) and the coordinates of the second point are (x₂, y₂) = (6, 6).

Applying the slope formula:

slope = (6 - 4) / (6 - 2)
slope = 2 / 4
slope = 1/2

Therefore, the slope of the line passing through the points (2, 4) and (6, 6) is 1/2.

(2, 5) (2, 2)

To find the slope of the line passing through the points (2, 5) and (2, 2), we can use the slope formula:

slope = (difference in y-coordinates) / (difference in x-coordinates)

Let's call the coordinates of the first point (x₁, y₁) and the coordinates of the second point (x₂, y₂). In this case, the coordinates are (2, 5) for the first point and (2, 2) for the second point.

Using the formula, we can calculate the slope:

slope = (2 - 5) / (2 - 2)
slope = -3 / 0

The difference in x-coordinates is 0, which means the denominator is 0. Dividing by 0 is undefined, so the slope of the line passing through the points (2, 5) and (2, 2) does not exist. This means the line is vertically oriented and parallel to the y-axis.

(-1, -2) (2, -2)

To find the slope of the line passing through the points (-1, -2) and (2, -2), we can use the slope formula:

slope = (difference in y-coordinates) / (difference in x-coordinates)

Let's call the coordinates of the first point (x₁, y₁) and the coordinates of the second point (x₂, y₂). In this case, the coordinates are (-1, -2) for the first point and (2, -2) for the second point.

Using the formula, we can calculate the slope:

slope = (-2 - (-2)) / (2 - (-1))
slope = (-2 + 2) / (2 + 1)
slope = 0 / 3
slope = 0

Therefore, the slope of the line passing through the points (-1, -2) and (2, -2) is 0. The line is horizontal and parallel to the x-axis.