Question

What is the slope intercept form of a line that passes through (-6,5) and is perpendicular to the graph of 2x-y=5?

Answer 1

$\text{The slope-intercept form}\ y=mx+b.\\\\Let\\k:y=m_1x+b_1\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\\------------------------\\2x-y=5\to y=2x-5\\\\\text{Let}\ k:y=2x-5\ \text{and}\ l:y=mx+b\\\\l\ \perp\ k\iff2m=-1\qquad|:2\to m=-\dfrac{1}{2}\\\\l:y=-\dfrac{1}{2}x+b\\\\\text{Substitute the coordinates of the point (-6, 5) to the equation}\\\text{of the line}\ l:\\\\5=-\dfrac{1}{2}(-6)+b\\5=3+b\qquad|-3\\2=b\to b=2\\\\\boxed{Answer:\ y=-\dfrac{1}{2}x+2}$