Question

How to write an equation of the line through the point (-2,1) that is perpendicular to the line 5x+9y=-9

Answer 1

`\large\boxed{y=(5)/(9)x+(19)/(9)}`

Explanation:

`\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-(1)/(m_1)\\\\l\ \parallel\ k\iff m_1=m_2\\\\===================================\\\\\text{We have the equation i the standard form.}\\\text{ Convert it to the slope-intercept form}\ y=mx+b:\\\\5x+9y=-9\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\9y=-5x-9\qquad\text{divide both sides by 9}\\\\y=-(5)/(9)x-1\to m_1=-(5)/(9)\\\\m_2=-(1)/(m_1)\to m_2=-(1)/(-(5)/(9))=(9)/(5)`

`\text{We have the equation:}\\\\y=(5)/(9)x+b\\\\\text{Put the coordinates of the point (-2, 1) to the equation:}\\\\1=(5)/(9)(-2)+b\\\\1=-(10)/(9)+b\qquad\text{add}\ (10)/(5)\ \text{to both sides}\\\\(19)/(9)=b\to b=(19)/(9)`