Answer:
y = 2x-4
Explanation:
This has already been answered correctly by aechristman27, but I'll add some of the details.
The equation of a line perpendicular to a reference equation has a slope that is the negative inverse of the referenced line's slope.
Reference line:
We are only given two points on the reference line. We need the slope of this line, which we can find from the two given points.
The slope is the Rise/Run (The change in y for a change in x)
Use the two points:
(2,6) and (6,4)
Rise = (4-6) = -2
Run = (6-2 = 4
Slope = Rise/Run = -2/4 or -(1/2)
The new slope is the negative inverse of -(1/2), which makes the new slope 2.
The new line is then y = 2x + b.
To find b, we can use the one given point on this line: (-1,-6). Enter that point ion the equation and solve for b:
y = 2x + b
-6 = 2(-1) + b for (-1,-6)
-6 = -2 + b
b = -4
The equation is y = 2x-4
See the attached graph.