Question

PLEASE HURRY

line passes through (8,-6) and perpendicular to the line 2x+y= -7
slope of line p is -1/2
what is the equation of line p is y = 1/2x +

Answer 1

`\large\boxed{y=(1)/(2)x-10}`

Explanation:

`\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 equation of a line in standard form}\ Ax+By=C.\\\text{Convert to the slope-intercept form}\ y=mx+b\\\\2x+y=-7\qquad\text{subtract 2x from both sides}\\\\y=-2x-7\to m_1=-2\\\\\text{Therefore}\ m_2=-(1)/(-2)=(1)/(2).\\\\\text{We have the equation}\ y=(1)/(2)x+b.`

`\text{The line passes through the point (8, -6). Put the coordinates of this}\\\text{point to the equation and solve}\ b:\\\\-6=(1)/(2)(8)+b\\\\-6=4+b\qquad\text{subtract 4 from both sides}\\\\-10=b\to b=-10\\\\\text{Finally we have:}\ y=(1)/(2)x-10`