Question

Please help me with this step by step.

Answer 1

`\large\boxed{y=-(1)/(5)x+(3)/(5)}`

Explanation:

`\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-\text{slope}\\b-\text{y-intercept}\\\\\text{Let}\\\\k:y=m_1x+b_1\\l:y=m_2x+b_2\\\\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+2\to m_1=5\\\\\text{therefore}\ m_2=-(1)/(5).\\\\\text{Put the value of a slope and the coordinates of the given point}\ (-2,\ 1)\\\text{to the equation of a line}\ y=mx+b:\\\\1=-(1)/(5)(-2)+b\\\\1=(2)/(5)+b\qquad\text{subtract}\ (2)/(5)\ \text{from both isdes}\\\\1-(2)/(5)=(2)/(5)-(2)/(5)+b\\\\(5)/(5)-(2)/(5)=b\to b=(3)/(5)\\\\\text{Finally:}\\\\y=-(1)/(5)x+(3)/(5)`