The calculated slope, -1/2, signifies a consistent 1/2 unit decrease in y for every 1-unit increase in x. This negative slope illustrates the inverse relationship between the variables in this linear context.
In the given example, the slope of the line can be determined using the formula:
m = Δy/Δx
Considering the points (-4, 0) and (0, -2), the vertical change (Δy) is -2 (final y - initial y), and the horizontal change (Δx) is 4 (final x - initial x). Plugging these values into the formula:
m = -2/4
Simplifying, we get \( m = -\frac{1}{2} \). This implies that for every 1-unit increase in x, the corresponding decrease in y is 1/2 units. The negative sign indicates a downward slope, showcasing the inverse relationship between the variables.
This information is essential for interpreting the linear connection between x and y, revealing that as x increases, y decreases at a consistent rate. The slope, represented as a fraction, is -1/2, encapsulating the quantitative aspect of this linear relationship.