What is the equation of the line perpendicular to the line y=-x+2 through the point (3,5)

The equation of the line perpendicular to the line y=-x+2 through the point (3,5) is y = x + 2

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial value of y.

Two lines are said to be perpendicular if the product of their slope is -1. That is the slope of one line is the negative inverse of the other line.

Given the line y = -x + 2. The slope of the line is -1.

The slope of a line perpendicular is 1 (negative inverse of -1).

Hence:

The equation of the line perpendicular to the line y=-x+2 through the point (3,5) is y = x + 2

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