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Find slope of a line going through points (-5,2) and (6,-9)

User Fuiiii
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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.

User Jack Chern
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