The equation of the perpendicular line is y = x + 2.
To find the perpendicular line through the point (2,4) and perpendicular to the line y = -x + 5, we need to determine the slope of the given line and then find the negative reciprocal of that slope.
The given line has a slope of -1, so the slope of the perpendicular line will be 1.
Using the point (2,4) and slope 1, we can use the point-slope form of a line to write the equation of the perpendicular line as y - 4 = 1(x - 2), or y = x + 2.
Therefore, the equation of the perpendicular line through (2,4) is y = x + 2.
The probable question may be:
Find the Perpendicular Line through: (2,4) , perp. to y=-x+5