What is the intersection point of the line y = -2x + 5 and the line perpendicular to it that passes through the point (5,5)?
Perpendicular: Product of slopes = -1.
Let m be the slope of the line perpendicular to y = -2x + 5.
Slope of y = -2x + 5 is -2.
This means \(-2\cdot m = -1\), i.e., \(m = \dfrac12\).
The required line passes through (5, 5) and the slope is 1/2. We use the point-slope form of the equation of a straight line.
The equation of the required line is
\(y - 5 = \dfrac12 \left(x - 5\right)\\ 2y - 10 = x - 5\\ \boxed{x - 2y + 5 = 0}\)