Answer:
[tex]y=2x-4[/tex]
Step-by-step explanation:
step 1
Find the slope of the given line
we have
[tex]y=-\frac{1}{2}x+3[/tex]
This is the equation of the line in slope intercept form
The slope is [tex]m=-\frac{1}{2}[/tex]
step 2
Find the slope of the line perpendicular to the given line
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
we have
[tex]m=-\frac{1}{2}[/tex] ----> slope of the given line
therefore
The opposite reciprocal is
[tex]m=2[/tex]
step 3
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=2[/tex]
[tex]point\ (2,0)[/tex]
substitute
[tex]y-0=2(x-2)[/tex]
Convert to slope intercept form
[tex]y=2x-4[/tex]
see the attached figure to better understand the problem
