Question

Find the equation of the line that is perpendicular to the line 4x + 2y = 1 and passes through the point (−4, 3).

Answer 1

`\large\boxed{y=(1)/(2)x+5}`

Explanation:

`\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-(1)/(m_1)\\============================\\\\\text{We have}\ 4x+2y=1.\ \text{Convert to the slope-intercept form y = mx + b:}\\\\4x+2y=1\qquad\text{subtract 4x from both sides}\\\\2y=-4x+1\qquad\text{divide both sides by 2}\\\\y=-2x+(1)/(2)\to m_1=-2.\\\\\text{Therefore}\ m_2=-(1)/(-2)=(1)/(2).\\\\\text{The equation of the searched line:}\ y=(1)/(2)x+b.\\\\\text{The line passes through }(-4,\ 3).`

`\text{Put the coordinates of the point to the equation.}\ x=-4,\ y=3:\\\\3=(1)/(2)(-4)+b\\\\3=-2+b\qquad\text{add 2 to both sides}\\\\b=5`