Question

Write the slope-intercept form of the equation of the line described.

through:(-2,-4), perpendicular to y=2x+5

Answer 1

Find the negative reciprocal of the slope of the original line and use the slope-intercept form

y=mx+b to find the line perpendicular to
`y=2x+5`.

`y=−12x−5`

Hope this helps!!

Answer 2

`\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}\ k:y=2x+5\to m_1=2.\\\\l:y=mx+b\to m=-(1)/(2)\to y=-(1)/(2)x+b.\\\\\text{The line passes through the point (-2, -4).}\ \text{Put the coordinates to the equation:}\\\\-4=-(1)/(2)(-2)+b\\\\-4=1+b\qquad\text{subtract 1 from both sides}\\\\-5=b\to b=-5\\\\Answer:\ \boxed{y=-(1)/(2)x-5}`