Question

What is the equation of a line that passes through the point (2,7) and is perpendicular to the line whose equaton is y=x/4 +5

Answer 1

`Let\ k:y=m_1x+b_1\ and\ l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\\\\We\ have\ k:y=(x)/(4)+5=(1)/(4)x+5\to m_1=(1)/(4).\\\\Let\ l:y=mx+b\\\\l\ \perp\ k\iff(1)/(4)m=-1\qquad|\cdot4\to m=-4\\\\l:y=-4x+b.\\\\The\ line\ l\ passes\ through\ the\ point\ (2,\ 7).\ Substitute\ the\ coordinates\\to\ the\ equation\ of\ the\ line\ l:\\\\7=-4(2)+b\\7=-8+b\qquad|+8\\15=b\to b=15\\\\Answer:\ \boxed{y=-4x+15}`