A line passes through the point (5, 7) and has a slope of -1. What is the equation of the line?
y = -x + 12
We need the equation of a straight line passing through the point \((5, 7)\) with slope \(m = -1\).
The most direct tool is the point-slope form of a line: \(y - y_{1} = m(x - x_{1})\).
Here \((x_{1}, y_{1}) = (5, 7)\) and \(m = -1\).
Substituting these values: \(y - 7 = -1(x - 5)\).
Expand the right side: \(y - 7 = -x + 5\).
Add 7 to both sides to isolate \(y\): \(y = -x + 5 + 7 = -x + 12\).
The key concept is the point-slope form, which builds a line's equation directly from one point and the slope.
Hence the equation of the line is y = -x + 12.
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