Question

Which of the following equations represents a line that is perpendicular to

y = -2x+4 and passes through the point, (4, 2)?

Answer 1

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

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:}\ y=-2x+4\to m_1=-2.\\\\\text{Therefore}\ m_2=-(1)/(-2)=(1)/(2).\\\\\text{We have the equation:}\ y=(1)/(2)x+b.\\\\\text{Put the coordinate of the point (4, 2) to the equation:}\\\\2=(1)/(2)(4)+b\\\\2=2+b\qquad\text{subtract 2 from both sides}\\\\0=b\to b=0.\\\\\text{Finally:}\\\\y=(1)/(2)x`