Answer:
9x +2y = 0
Step-by-step explanation:
You want the equation of a line perpendicular to one through points (0, 4) and (9, 6).
Perpendicular line
When a line goes through points (x1, y1) and (x2, y2), the equation of a perpendicular line can be written as ...
(x2 -x1)x +(y2 -y1)y = 0
For the points (0, 4) and (9, 6), the perpendicular line will be ...
(9 -0)x +(6 -4)y = 0
9x +2y = 0 . . . . . equation of a perpendicular line
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Additional comment
If the line must go through a particular point (h, k), then the equation can be translated to that point by ...
(x2 -x1)(x -h) +(y2 -y1)(y -k) = 0
As you will notice in the attachment, the above equation gives a line that goes through the origin, (h, k) = (0, 0).
The slope of a line through two points (x1, y1) and (x2, y2) is calculated as ...
m = (y2 -y1)/(x2 -x1)
A perpendicular line will have a slope that is the opposite reciprocal of this:
m' = -1/m = -(x2 -x1)/(y2 -y1)
A line with the equation ax +by = c has a slope that is -a/b. The above line with equation (x2 -x1)x +(y2 -y1)y = 0 will have a slope of
-(x2 -x1)/(y2 -y1)
Comparing this to m', you see this is the slope of a perpendicular to the line through (x1, y1), (x2, y2).
We could have used any two points from the given table. We chose to use the two points with the smallest non-negative x-values.
