Answer:
y = -1/2x +5/2
Step-by-step explanation:
The equation of the desired line can be determined by first finding the slope of the line between the two reference points. Then the point-slope equation of the desired line can be written, and that can be rearranged to slope-intercept form.
__
The slope of the line between two points is given by the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (18 -12)/(5 -2) = 6/3 = 2
The slope of the perpendicular line is the opposite reciprocal of this:
m' = -1/m = -1/2
__
The point-slope equation of a line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
The line we want can be described by the equation ...
y -1 = -1/2(x -3) . . . . . line with slope -1/2 through point (3, 1)
__
Rearranging to slope-intercept form, we find ...
y = -1/2x +3/2 +1
y = -1/2x +5/2
_____
Additional comment
The geometry program used to draw the figure in the attachment shows the line's equation in standard form to be ...
x +2y = 5
Solving for y gives the slope-intercept equation:
2y = -x +5 . . . . . . . . subtract x
y = -1/2x +5/2 . . . . . divide by 2
