Question

Help with this problem!! Please help ASAP!!

Answer 1

`\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2\\\\l\perp k\iff m_1m_2=-1\to m_2=-(1)/(m_1)\\\\\text{We have the points B(6, 9) and C(8, -7)}.\\\\\text{The formula of a slope:}\\\\m=(y_2-y_1)/(x_2-x_1)\\\\\text{substitute:}\\\\m_1=(-7-9)/(8-6)=(-16)/(2)=-8\\\\\text{therefore}\ m_2=-\frac{1}8}=-(1)/(8)\\\\\text{The formula of a midpoint:}\\\\\left((x_1+x_2)/(2);\ (y_1+y_2)/(2)\right)\\\\\text{substitute the coordinates of the points B and C:}`

`x=(6+8)/(2)=(14)/(2)=7\\\\y=(9+(-7))/(2)=(2)/(2)=1\\\\\text{midpoint}\ (7,\ -1)\\\\\text{The point-slope form:}\\\\y-y_1=m(x-x_1)\\\\\text{Substitute}\ m=-(1)/(8),\ x_1=7\ \text{and}\ y_1=1:\\\\\boxed{y-1=-(1)/(8)(x-7)}`