Question

Perpendicular to 3x-6y=-2 containing points (-3,-8)

Answer 1

y = -2x - 14

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 the equation of a line in the standard form.}\\\text{Convert it to the slope intercept from:}\\\\3x-6y=-2\qquad\text{subtract }\ 3x\ \text{from both sides}\\\\-6y=-3x-2\qquad\text{divide both sides by (-6)}\\\\y=(-3)/(-6)x+(-2)/(-6)\\\\y=(1)/(2)x+(1)/(3)\to m_1=(1)/(2)`

`\text{Therefore}\ m_2=-(1)/((1)/(2))=-1\cdot(2)/(1)=-2.\\\\\text{Put the value of a slope and the coordinates of the point (-3, -8)}\\\text{ to the equation of a line:}\\\\-8=-2(-3)+b\\\\-8=6+b\qquad\text{subtract 6 from both sides}\\\\-14=b\to b=-14\\\\\text{Finally:}\\\\y=-2x-14`