Question

Write an equation for a line perpendicular to

y=5x−1
and passing through the point (15,2)

Answer 1

`\large\boxed{y=-(1)/(5)x+5}`

Explanation:

`\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\\text{then}\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-(1)/(m_1)\\\\k\ ||\ l\iff m_1=m_2`

`\text{We have}\ y=5x-1\to m_1=5.\\\\\text{therefore}\ m_2=-(1)/(5).\\\\y=-(1)/(5)x+b\\\\\text{Substitute the coordinaes of the given point (15, 2):}\\\\2=-(1)/(5)(15)+b\\\\2=-3+b\qquad\text{add 3 to both sides}\\\\5=b\to b=5\\\\\bold{FINALLY:}\\\\y=-(1)/(5)x+5`