Answer:
[tex]y+3=-2(x-5)[/tex]
Step-by-step explanation:
We need an equation of the line perpendicular to the given line
[tex]y=\frac{1}{2}x+4[/tex]
if we compare this equation with the standard form:
[tex]y=mx+c[/tex]
m equals 1/2 and c=4 , we do not c (y-intercept) in our calculation so just ignore it.
Furthermore the slope of the perpendicular line is given by the formula:
[tex]m_1m_2=-1\\[/tex]
where our [tex]m_1=1/2[/tex] and m2 is the slope of the perpendicular line so,
[tex]m_1m_2=-1\\\\\frac{1}{2} m_2=-1\\\\m_2=-2[/tex]
we have the slope of the perpendicular line which is -2 and the point P is given to us which is (5,-3) , so we use the equation of point-slope form:
[tex]y-y_1=m(x-x_1)\\y-(-3)=-2(x-5)\\y+3=-2x+10\\y=-2x+7\\[/tex]
we need our answer in point-slope form so it would be
[tex]y+3=-2(x-5)[/tex]
