Answer:
Option A) y = -2x + 15
Step-by-step explanation:
step 1
Find the slope of the line perpendicular to the given line
we know that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
The equation of the given line is
[tex]y=\frac{1}{2}x+3[/tex]
so
The slope of the given line is [tex]m=\frac{1}{2}[/tex]
therefore
The slope of the line perpendicular to the given line is
[tex]m=-2[/tex]
step 2
Find the equation of the perpendicular line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-2[/tex]
[tex]point\ (10,-5)[/tex]
substitute
[tex]y+5=-2(x-10)[/tex] ---> equation in point slope form
Convert to slope intercept form
[tex]y=mx+b[/tex]
[tex]y+5=-2x+20[/tex]
[tex]y=-2x+20-5[/tex]
[tex]y=-2x+15[/tex]
