Final Answer:
The slope of the line going through the points (-5,2) and (6,-9) is -1.
Step-by-step explanation:
To find the slope (m) of a line passing through two points((x₁, y₁) and ((x₂, y₂), you can use the formula:
m = {y₂ - y₁}/{x₂ - x₁]
For the given points (-5,2) and (6,-9), substitute the coordinates into the formula:
m = {(-9) - 2}/{6 - (-5)
Simplify the expression:
m =-11/11
Finally, reduce the fraction:
m = -1
Therefore, the slope of the line passing through (-5,2) and (6,-9) is -1. This means that for every unit increase in (x), the (y)-value decreases by 1.
Understanding the slope of a line is crucial in graphing and analyzing linear relationships. In this context, a slope of -1 signifies a downward slope. It indicates that as you move from left to right along the line, the \(y\)-values decrease. This insight is valuable in interpreting the behavior of the line in the given coordinate system. In real-world applications, the slope represents the rate of change, helping to understand the relationship between two variables represented by the coordinates. In the case of this line, the slope of -1 provides a clear and concise description of its directional characteristics.