Question

Write an equation of the line that is perpendicular to y = 1 2 x + 3 and passes through the point (10, -5). A) y = -2x + 15 B) y = 2x - 15 C) y = -2x - 5 D) y = - 1 2 x

Answer 1

`\large\boxed{A)\ y=-2x+15}`

Explanation:

`\text{Let}\ k:y=_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}\ y=(1)/(2)x+3\to m_1=(1)/(2).\\\\\text{Therefore}\ m_2=-(1)/((1)/(2))=-2.\\\\\text{The equation of the searched line:}\ y=-2x+b.\\\\\text{The line passes through }(10,\ -5).`

`\text{Put the coordinates of the point to the equation.}\ x=10,\ y=-5:\\\\-5=-2(10)+b\\\\-5=-20+b\qquad\text{add 20 to both sides}\\\\b=15`