Question

17. Write the equation of a line that is perpendicular to the given line and that passes through the given point.

y - 2 = 7/3 (x + 5); (-4, 9)

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 line in point-slope form:}\\\\y-y_1=m(x-x_1)\\\\m-slope\\\\y-2=(7)/(3)(x+5)\to m_1=(7)/(3)\\\\\text{therefore}\ m_2=-(1)/((7)/(3))=-(3)/(7).\\\\\text{We have the slope}\ m=-(3)/(7)\ \text{and the point}\ (-4,\ 9).\ \text{Substitute:}\\\\y-9=-(3)/(7)(x-4))\\\\\boxed{y-9=-(3)/(7)(x+4)}`