Question

Determine the slope between the points (-6, 1) and (-6, -4).

Answer 1

The slope between the points (-6, 1) and (-6, -4) is undefined.

Step-by-step explanation:

The slope (m) between two points (x₁, y₁) and (x₂, y₂) is calculated using the formula
`\(m = \frac{{y₂ - y₁}}{{x₂ - x₁}}\)`. In this case, the x-coordinates of the given points are the same, i.e., x₁ = x₂ = -6. Therefore, the denominator becomes 0, resulting in an undefined slope. This condition occurs when the line is vertical, and the change in x is zero. In the context of the given points (-6, 1) and (-6, -4), the line connecting them is vertical, and thus, the slope is undefined.

Understanding the concept of slope is crucial in analyzing the steepness or direction of a line. A vertical line has an undefined slope, as there is no change in x, and the line goes straight up or down. In contrast, a horizontal line has a slope of 0, indicating that there is no change in y.

Recognizing the characteristics of different slopes contributes to a deeper understanding of the geometric properties of lines on a coordinate plane. In this specific case, the undefined slope emphasizes the vertical orientation of the line passing through the points (-6, 1) and (-6, -4).

Answer 2

The slope between the points (-6, 1) and (-6, -4) is undefined. In this case, the x-coordinates of the two points are the same, resulting in a vertical line. The formula for slope (change in y divided by change in x) becomes division by zero, leading to an undefined slope.

Step-by-step explanation:

The slope between the points (-6, 1) and (-6, -4) is undefined.

The reason for this is that the two points lie on a vertical line, where the change in the x-coordinates is zero.

The formula for slope (change in y divided by change in x) involves division by zero in this case, making the slope undefined.

In general, a vertical line has an undefined slope, as it rises or falls infinitely without any horizontal movement.

It's crucial to recognize this special case and understand that the concept of slope doesn't apply to vertical lines in the traditional sense due to the division by zero issue.