Answer: y = -(4/3)x + 1
Explanation:
Let's start with finding an equation of a straight line (y=mx+b) that goes through points (-2,1) and (6,7).
The slope of a line, m, is the change in y for the change in x, or Rise/Run.
This is derived from the two points.
Rise (7-1) = 6
Run (6 - (-2)) = 8
Rise/Run = 6/8 or 3/4
The line is therefore y = (3/4)x + b
Find b by using one of the two points. I'll use (-2,1), but the other would also work.
y = (3/4)x + b
1 = (3/4)(-2) + b
1 = -(6/4) + b
b = 10/4
The line becomes y = (3/4)x + 10/4
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A line perpendicular to this will have a slope that is the negative inverse of the original line. The negative inverse of (3/4) is -(4/3).
The perpendicular line will be:
y = -(4/3)x + b
Use point (-6,9) to find b:
y = -(4/3)x + b
9 = -(4/3)*(-6) + b
9 = (24/3) + b
b = (27/3 - 24/3) = 3/3 = 1
The line is y = -(4/3)x + 1