Answer :
The general equation of a line with slope m that passes through a point (x_0,y_0) is:
[tex]y=m(x-x_0)+y_0[/tex]On the other hand, two lines are perpendicular if their slopes m_1 and m_2 satisfy the contition:
[tex]m_1\cdot m_2=-1[/tex]Using the slope formula, determine the slope of the line that passes through the points (-6,8) and (10,0):
[tex]m_2=\frac{8-0}{-6-10}=\frac{8}{-16}=-\frac{1}{2}[/tex]A line perpendicular to that, will have a slope of:
[tex]m_1=-\frac{1}{m_2}=-\frac{1}{(-\frac{1}{2})}=2[/tex]Substitute the value for m_1 and the coordinates (4,5) in the general equation for a line with a given slope that passes through a given point:
[tex]\begin{gathered} y=m(x-x_0)+y_0 \\ \Rightarrow \\ y=2(x-4)+5 \end{gathered}[/tex]