Answer:
The equation \(y = x - 4\) represents a line with a slope of 1 (since the coefficient of \(x\) is 1), and the y-intercept is -4.
To find a line perpendicular to \(y = x - 4\), we need to consider that the slope of a line perpendicular to a given line is the negative reciprocal of the slope of that line.
The slope of \(y = x - 4\) is 1, so the slope of a line perpendicular to it will be \(-1\) (negative reciprocal of 1).
Now, using the point-slope form of a line (\(y - y_1 = m(x - x_1)\)) where \((x_1, y_1)\) is the given point (-7, -5) and \(m\) is the slope (-1):
\(y - (-5) = -1 \cdot (x - (-7))\)
\(y + 5 = -1 \cdot (x + 7)\)
\(y + 5 = -x - 7\)
Now, solve for \(y\):
\(y = -x - 7 - 5\)
\(y = -x - 12\)
Therefore, the equation of the line perpendicular to \(y = x - 4\) and passing through the point (-7, -5) is \(y = -x - 12\).
Explanation: