Answer:
[tex]y=-2x+8[/tex]
Step-by-step explanation:
Remember
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes are equal to -1)
The slope of the given line is m=1/2
so
the opposite reciprocal is m=-2
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-2\\point\ (7,-6)[/tex]
substitute
[tex]y+6=-2(x-7)[/tex]
Convert to slope intercept form
[tex]y=mx+b[/tex]
isolate the variable y
[tex]y+6=-2x+14[/tex]
[tex]y=-2x+14-6[/tex]
[tex]y=-2x+8[/tex]
