Answer:
y = 1/2x +4
Explanation:
The perpendicular line will have a slope that is the opposite reciprocal of the slope of the given line. The hint suggests a useful approach to answering the question.
Slope of given line
The equation of the given line is ...
y = -2x +5
Comparing this to the slope-intercept form of the equation for a line ...
y = mx +b
we see that the slope (m) is -2, and the y-intercept (b) is +5. Only the slope is of interest in this problem.
Slope of a perpendicular line
The slopes of perpendicular lines are opposite reciprocals of each other. That means the slope (m') of the perpendicular line will be ...
m' = -1/m
m' = -1/(-2) = 1/2
Point-slope form
The point-slope form of the equation of a line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
For the perpendicular line, the slope is m=1/2, and the point is (h, k) = (-4, 2). Using these values, we find the point-slope equation of the perpendicular line to be ...
y -2 = (1/2)(x -(-4))
Slope-intercept form
Adding 2 and simplifying the point-slope equation, we find ...
y = 1/2x +1/2(4) +2
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Additional comment
We have used m' for the slope of the perpendicular line in order to avoid confusion with the slope m of the given line it is perpendicular to. That value (m'=1/2) becomes the slope m in the point-slope equation for the perpendicular line. At that last step in the solution process, the original given line's slope of -2 is no longer of interest and can be forgotten. (In short, the variable "m" in the last step means something different from its original use in the first step of the solution process. We expect you will understand and not be confused by this.)