Final Answer:
The slope of a line with m = -1 is equal to -1.
Step-by-step explanation:
The slope m of a line represents the ratio of the vertical change Delta y to the horizontal change Delta x between any two points on the line. In mathematical terms,
). When the slope is given as m = -1 , it means that for every unit increase in the horizontal direction Delta x , there is a corresponding unit decrease in the vertical direction Delta y . This relationship creates a downward-sloping line, indicating a negative slope.
Slope is often visualized as the rise over run. In the case of m = -1 , for every one unit run to the right, there is a one unit drop downwards. The negative sign signifies the downward direction. Another way to interpret this is that as you move from left to right along the line, the y-coordinates decrease by one unit for every increase of one unit in x. This creates a line that slopes downward at a 45-degree angle. The steepness of the slope is determined by the magnitude of m, and in this case, it is 1, making the line relatively steep. Therefore, a slope of m = -1 describes a line that descends at a 45-degree angle from left to right.